Bifurcation from infinity for an asymptotically linear Schrödinger equation

Authors: Wojciech Kryszewski, Andrzej Szulkin

Source: Journal of Fixed Point Theory and Applications. 16:411-435

Subject Terms: Variational methods for second-order elliptic equations, 4. Education, Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian, Schrödinger equation, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, 16. Peace & justice, 01 natural sciences, bifurcation from infinity, Mathematics - Analysis of PDEs, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, 35J20, 35J91, 58E05, 58E07, asymptotically linear, FOS: Mathematics, Morse theory, 0101 mathematics, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/1412.1310
http://www.diva-portal.org/smash/record.jsf?pid=diva2:821614
https://link.springer.com/article/10.1007/s11784-015-0221-8
https://link.springer.com/content/pdf/10.1007%2Fs11784-015-0221-8.pdf

Bifurcations of extremals of Fredholm functionals

Authors: Sergey L’vovich Tsarev, Yuri Ivanovich Sapronov, B. M. Darinskii

Source: Journal of Mathematical Sciences. 145:5311-5453

Subject Terms: Research exposition (monographs, survey articles) pertaining to operator theory, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Group-invariant bifurcation theory in infinite-dimensional spaces, Applications of operator theory to differential and integral equations, Catastrophe theory, Equations involving nonlinear operators (general), 0103 physical sciences, 0101 mathematics, Abstract bifurcation theory involving nonlinear operators, Homotopy and topological questions for infinite-dimensional manifolds, Thin bodies, structures, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/5076926
https://doi.org/10.1007/s10958-007-0356-2
https://link.springer.com/article/10.1007%2Fs10958-007-0356-2
https://link.springer.com/content/pdf/10.1007/s10958-007-0356-2.pdf

A generalized-degree homotopy yielding global bifurcation results

Authors: Stewart C. Welsh

Source: Nonlinear Analysis: Theory, Methods & Applications. 62:89-100

Subject Terms: Fréchet derivative, \(A\)-proper operators, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, nonlinear eigenvalue problem, 0211 other engineering and technologies, generalized topological degree, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc, Fredholm operator of index zero, 02 engineering and technology, 0101 mathematics, Abstract bifurcation theory involving nonlinear operators, 01 natural sciences, global bifurcation point

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Access URL: https://www.sciencedirect.com/science/article/pii/S0362546X05002373

Solutions of Multiparameter Systems of Elliptic Differential Equations: Solutions of multiparameter systems of elliptic differential equations

Authors: Joanna Gawrycka, Sławomir Rybicki

Source: Advanced Nonlinear Studies. 5:279-302

Subject Terms: Bifurcations in context of PDEs, Degree theory for nonlinear operators, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Variational methods for elliptic systems, 0101 mathematics, Abstract bifurcation theory involving nonlinear operators, 10. No inequality, 16. Peace & justice, 01 natural sciences

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Access URL: https://www.degruyter.com/document/doi/10.1515/ans-2005-0207/xml

Bifurcation problems for superlinear elliptic indefinite equations with exponential growth

Authors: Adimurthi, Jacques Giacomoni

Source: Nonlinear Differential Equations and Applications NoDEA. 12:1-20

Subject Terms: Bifurcations in context of PDEs, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, superlinear elliptic problem, Nonlinear elliptic equations, 0101 mathematics, global bifurcation, sign-changing nonlinearity, 01 natural sciences

File Description: application/xml

Access URL: https://www.infona.pl/resource/bwmeta1.element.springer-8a2eb103-59ae-34ea-a54d-14ae87e2fa28
https://rd.springer.com/article/10.1007/s00030-004-1057-x
https://link.springer.com/article/10.1007%2Fs00030-004-1057-x
https://link.springer.com/10.1007/s00030-004-1057-x

Parabolic sets and caustics for parametric families of Fredholm functionals

Authors: E. V. Chemerzina

Source: Journal of Mathematical Sciences. 126:1664-1668

Subject Terms: Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Catastrophe theory, 0103 physical sciences, Abstract bifurcation theory involving nonlinear operators, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/2193570
https://doi.org/10.1007/s10958-005-0056-8
https://link.springer.com/article/10.1007/s10958-005-0056-8

Atypical Bifurcation Without Compactness: Atypical bifurcation without compactness

Authors: BENEVIERI, PIERLUIGI, FURI, MASSIMO, M. Martelli, PERA, MARIA PATRIZIA

Source: Zeitschrift für Analysis und ihre Anwendungen. 24:137-147

Subject Terms: Nonlinear Functional Analysis, Bifurcation Theory, Fredholm Operators, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Degree theory for nonlinear operators, global bifurcations, Applied Mathematics, 0103 physical sciences, 0101 mathematics, Abstract bifurcation theory involving nonlinear operators, oriented Fredholm maps, 01 natural sciences, Analysis, topological degree

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Access URL: https://zbmath.org/2186773
https://doi.org/10.4171/zaa/1233
https://ems.press/journals/zaa/articles/890
https://ems.press/content/serial-article-files/925
https://www.ems-ph.org/doi/10.4171/ZAA/1233
https://www.ems-ph.org/journals/show_pdf.php?issn=0232-2064&vol=24&iss=1&rank=6
https://www.openaccessrepository.it/record/153120
https://hdl.handle.net/2158/307019
https://doi.org/10.4171/ZAA/1233

A bifurcation result for semi-Riemannian trajectories of the Lorentz force equation

Authors: PICCIONE PAOLO, PORTALURI, Alessandro

Source: Journal of Differential Equations. 210:233-262

Subject Terms: Lorentz force equation, 58E10, 58J55, 53D12, 34K18, 47A53, Bifurcation theory for PDEs on manifolds, 01 natural sciences, Functional Analysis (math.FA), Mathematics - Functional Analysis, Lagrangian submanifolds, Maslov index, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Mathematics - Classical Analysis and ODEs, 0103 physical sciences, Spectral flow, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Bifurcation, (Semi-) Fredholm operators, index theories, 0101 mathematics, Bifurcation theory of functional-differential equations, Analysis

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Access URL: http://arxiv.org/abs/math/0312090
https://zbmath.org/2167765
https://doi.org/10.1016/j.jde.2004.11.007
https://www.sciencedirect.com/science/article/abs/pii/S0022039604005121
https://core.ac.uk/display/82743568
https://ui.adsabs.harvard.edu/abs/2005JDE...210..233P/abstract
https://www.sciencedirect.com/science/article/pii/S0022039604005121
https://hdl.handle.net/11587/327731

Discriminant sets and layerings of bifurcating solutions of fredholm equations: Discriminant sets and layerings of bifurcating solutions of Fredholm equations

Authors: Yu. I. Sapronov, B. M. Darinskii

Source: Journal of Mathematical Sciences. 126:1297-1311

Subject Terms: Bifurcations in context of PDEs, nonlocal Lyapounov-Schmidt method, cristalline ferroelectrics, Bifurcations of singular points in dynamical systems, nonlinear Fredholm mappigs, Poincaré-Andronov-Hopf bifurcation, Cacciopoli scheme, elastic and crystalline media, 01 natural sciences, Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, nonlinear problems, Numerical bifurcation problems, Bifurcations of limit cycles and periodic orbits in dynamical systems, 0103 physical sciences, Computational methods for bifurcation problems in dynamical systems, 0101 mathematics, periodic waves, bifurcations

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Access URL: https://link.springer.com/article/10.1007/s10958-005-0098-y
https://link.springer.com/content/pdf/10.1007/PL00021961.pdf

A note on non-degenerate umbilics and the path formulation for bifurcation problems

Authors: Furter, Jacques-Elie, Sitta, Angela Maria

Contributors: Universidade Estadual Paulista (UNESP)

Source: Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 134:1115-1126

Subject Terms: Variational problems in abstract bifurcation theory in infinite-dimensional spaces, path formulation, Dynamical aspects of symmetries, equivariant bifurcation theory, umbilic singularities, 0101 mathematics, Abstract bifurcation theory involving nonlinear operators, 01 natural sciences, multiparametric bifurcation

File Description: application/xml

Access URL: https://zbmath.org/2141292
https://doi.org/10.1017/s0308210500003656
https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/note-on-nondegenerate-umbilics-and-the-path-formulation-for-bifurcation-problems/180D9A933857A306E23517D2A410FC6E
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0308210500003656
https://repositorio.unesp.br/handle/11449/68029
http://repositorio.unesp.br/handle/11449/68029

Bounded perturbations of homogeneous quasilinear operators using bifurcations from infinity

Authors: Petr Girg, Peter Takáč, Pavel Drábek

Source: Journal of Differential Equations. 204:265-291

Subject Terms: Bifurcations in context of PDEs, Perturbations in context of PDEs, p-Laplacian, Landesman–Lazer problem, Nonlinear elliptic equations, \(p\)-Laplacian, Vanishing nonlinearities, 01 natural sciences, Variational methods involving nonlinear operators, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Landesman--Lazer problem, Asymptotic bifurcation, 0101 mathematics, Analysis

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Access URL: https://zbmath.org/2117816
https://doi.org/10.1016/j.jde.2003.09.011
https://www.sciencedirect.com/science/article/pii/S0022039604002207
https://ui.adsabs.harvard.edu/abs/2004JDE...204..265D/abstract
https://core.ac.uk/display/82483057

On bifurcation, critical groups and exact multiplicity of solutions to semilinear elliptic boundary value problems

Authors: Zhitao Zhang

Source: Nonlinear Analysis: Theory, Methods & Applications. 58:535-546

Subject Terms: Bifurcations in context of PDEs, Boundary value problems for second-order elliptic equations, Variational methods involving nonlinear operators, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Bifurcation, Critical points, Nonlinear elliptic equations, 0101 mathematics, Abstract bifurcation theory involving nonlinear operators, Sign-changing solutions, 01 natural sciences, Critical groups

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Access URL: http://www.sciencedirect.com/science/article/pii/S0362546X04001932
https://www.sciencedirect.com/science/article/pii/S0362546X04001932

ON THE HESSIAN OF THE ENERGY FORM IN THE GINZBURG–LANDAU MODEL OF SUPERCONDUCTIVITY: On the Hessian of the energy form in the Ginzburg-Landau model of superconductivity

Authors: Comte, Myriam, Sauvageot, M.

Contributors: Ruprecht, Liliane

Source: Reviews in Mathematical Physics. 16:421-450

Subject Terms: Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Applications of variational problems in infinite-dimensional spaces to the sciences, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Statistical mechanics of superconductors

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Access URL: https://hal.science/hal-00018879v1
http://ui.adsabs.harvard.edu/abs/2004RvMaP..16..421C/abstract
https://www.worldscientific.com/doi/abs/10.1142/S0129055X04002059

Bifurcation of the Point of Equilibrium in Systems with Zero Roots of the Characteristic Equation: Bifurcation of the point of equilibrium in systems with zero roots of the characteristic equation

Authors: V. V. Basov

Source: Mathematical Notes. 75:297-314

Subject Terms: Bifurcations of singular points in dynamical systems, Bifurcation theory for ordinary differential equations, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, bifurcation of the point of equilibrium, multidimensional invariant tori, system of differential equations with a small parameter, perturbed differential system, 0101 mathematics, 01 natural sciences

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Access URL: https://zbmath.org/2121359
https://doi.org/10.1023/b:matn.0000023309.07316.66
https://link.springer.com/article/10.1023/B%3AMATN.0000023309.07316.66
https://link.springer.com/10.1023/B:MATN.0000023309.07316.66

Invariant Reduction of Partially Potential Branching Equations and Iterative Methods in the Problem on a Bifurcation Point with a Symmetry: Invariant reduction of partially potential branching equations and iterative methods in the problem on a bifurcation point with a symmetry

Authors: B. V. Loginov, Bülent Karasözen

Source: Differential Equations. 40:410-419

Subject Terms: invariant reduction, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Group-invariant bifurcation theory in infinite-dimensional spaces, 0211 other engineering and technologies, iterative methods, 02 engineering and technology, 0101 mathematics, Abstract bifurcation theory involving nonlinear operators, bifurcation point, 01 natural sciences, branching equation

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Access URL: https://zbmath.org/2176624
https://doi.org/10.1023/b:dieq.0000035778.88884.c7
https://link.springer.com/article/10.1023/B:DIEQ.0000035778.88884.c7

Computer assisted proof to symmetry-breaking bifurcation phenomena in nonlinear vibration

Authors: Tadashi Kawanago

Source: Japan Journal of Industrial and Applied Mathematics. 21:75-108

Subject Terms: Bifurcations in context of PDEs, Bifurcation theory for ordinary differential equations, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Vibrations in dynamical problems in solid mechanics, Dynamical aspects of symmetries, equivariant bifurcation theory, Numerical bifurcation problems, Nonlinear oscillations and coupled oscillators for ordinary differential equations, 0101 mathematics, Abstract bifurcation theory involving nonlinear operators, 01 natural sciences

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007%2FBF03167433

Bifurcation of Nonlinear Equations: II. Dynamic Bifurcation: Bifurcation of nonlinear equations. II: Dynamic bifurcation

Authors: Ma, Tian, Wang, Shouhong

Source: Methods Appl. Anal. 11, no. 2 (2004), 179-210

Subject Terms: Bifurcations in context of PDEs, Bifurcation theory for ordinary differential equations, dynamic bifurcation, 0209 industrial biotechnology, Applications of operator theory to differential and integral equations, periodic solutions, 02 engineering and technology, Nonlinear differential equations in abstract spaces, attractor bifurcation, Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems, 01 natural sciences, stability of bifurcating solutions, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, 0103 physical sciences, Attractors, Abstract bifurcation theory involving nonlinear operators, Periodic solutions to ordinary differential equations

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Access URL: http://www.intlpress.com/site/pub/files/_fulltext/journals/maa/2004/0011/0002/MAA-2004-0011-0002-a002.pdf
https://zbmath.org/2242774
https://doi.org/10.4310/maa.2004.v11.n2.a2
https://projecteuclid.org/download/pdf_1/euclid.maa/1119019653
https://intlpress.com/site/pub/pages/journals/items/maa/content/vols/0011/0002/a002/index.html
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https://projecteuclid.org/journals/methods-and-applications-of-analysis/volume-11/issue-2/Bifurcation-of-Nonlinear-Equations-II-Dynamic-Bifurcation/maa/1119019653.full
http://projecteuclid.org/euclid.maa/1119019653

Bifurcation of Nonlinear Equations: I. Steady State Bifurcation: Bifurcation of nonlinear equations. I: Steady state bifurcation

Authors: Ma, Tian, Wang, Shouhong

Source: Methods Appl. Anal. 11, no. 2 (2004), 155-178

Subject Terms: Bifurcation theory for ordinary differential equations, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Boundary value problems for second-order elliptic equations, steady-state bifurcation, 0101 mathematics, Abstract bifurcation theory involving nonlinear operators, eigenvalues with even multiplicity, transcritical bifurcation, spectral theorem, 01 natural sciences, saddle-node bifurcation

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https://www.intlpress.com/site/pub/pages/journals/items/maa/content/vols/0011/0002/a001/
https://projecteuclid.org/journals/methods-and-applications-of-analysis/volume-11/issue-2/Bifurcation-of-Nonlinear-Equations-I-Steady-State-Bifurcation/maa/1119019652.full
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http://projecteuclid.org/euclid.maa/1119019652

Variational bifurcation for quasilinear elliptic equations

Authors: CANINO, Annamaria

Source: Calculus of Variations and Partial Differential Equations. 18:269-286

Subject Terms: Bifurcations in context of PDEs, bifurcation and multiplicity, Variational methods for second-order elliptic equations, Variational methods involving nonlinear operators, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, quasilinear eigenvalue problem, lack of regularity, lack of compactness, Nonlinear elliptic equations, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007/s00526-003-0200-6

GLOBAL BIFURCATION FROM THE EIGENVALUES OF SOME SEMILINEAR BIHARMONIC EQUATIONS: Global bifurcation from the eigenvalues of some semilinear biharmonic equations

Authors: Zu-Chi Chen, Kun Zhao

Source: Nonlinear Evolution Equations and Dynamical Systems. :13-23

Subject Terms: Bifurcations in context of PDEs, Degree theory for nonlinear operators, Boundary value problems for higher-order elliptic equations, Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, Nonlinear elliptic equations, 0101 mathematics, Abstract bifurcation theory involving nonlinear operators, biharmonic operator, global bifurcation, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/2069609
https://zbmath.org/2069595
http://www.worldscientific.com/doi/abs/10.1142/9789812795366_0002
https://www.ijpam.eu/en/index.php/ijdea/article/view/1256