On the Lack of External Response of a Nonlinear Medium in the Second-Harmonic Generation Process: On the lack of external response of a nonlinear medium in the second-harmonic generation process

Authors: Fioralba Cakoni, Narek Hovsepyan, Matti Lassas, Michael Vogelius

Source: SIAM Journal on Mathematical Analysis. 57:1370-1405

Subject Terms: second-harmonic generation process, Mathematics - Analysis of PDEs, Semilinear elliptic equations, nonlinear optics, Scattering theory for PDEs, Boundary value problems for second-order elliptic systems, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, Lasers, masers, optical bistability, nonlinear optics, scattered field control, transmission eigenvalues

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Access URL: http://arxiv.org/abs/2401.00998
https://zbmath.org/8024074
https://doi.org/10.1137/24m1669700

Subelliptic p$p$‐Laplacian spectral problem for Hörmander vector fields: Subelliptic \(p\)-Laplacian spectral problem for Hörmander vector fields

Authors: Mukhtar Karazym, Durvudkhan Suragan

Source: Mathematische Nachrichten. 298:1184-1200

Subject Terms: subelliptic \(p\)-Laplacian, 35P30, 35H20, 35J92, 35R03, Analysis of PDEs, FOS: Mathematics, Subelliptic equations, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, Quasilinear elliptic equations with \(p\)-Laplacian, Hörmander vector fields, spectral problem, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2306.14829
https://zbmath.org/8035815
https://doi.org/10.1002/mana.202300513

Adaptive Finite Element Approximations of the First Eigenpair Associated with \({p}\)-Laplacian: Adaptive finite element approximations of the first eigenpair associated with \(p\)-Laplacian

Authors: Guanglian Li, Jing Li, Julie Merten, Yifeng Xu, Shengfeng Zhu

Source: SIAM Journal on Scientific Computing. 47:A374-A402

Subject Terms: Numerical methods for eigenvalue problems for boundary value problems involving PDEs, convergence, Error bounds for boundary value problems involving PDEs, 65N12, 65N25, 65N30, 65N50, 35P30, p-Laplacian, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, adaptive finite element method, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, \(p\)-Laplacian, FOS: Mathematics, Mathematics - Numerical Analysis, Quasilinear elliptic equations with \(p\)-Laplacian, first eigenvalue, a posteriori error estimator

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Access URL: http://arxiv.org/abs/2402.06889
https://zbmath.org/7988245
https://doi.org/10.1137/24m1637052
https://hdl.handle.net/11370/38fde517-5607-4324-a94f-59f28f4250e0
https://doi.org/10.1137/24M1637052
https://research.rug.nl/en/publications/38fde517-5607-4324-a94f-59f28f4250e0

Some inequalities between Laplacian eigenvalues on Riemannian manifolds

Authors: Huang, Guangyue, Wang, Botao, Qi, Xuerong

Source: Discrete and Continuous Dynamical Systems - S. 18:806-815

Subject Terms: Variational methods for higher-order elliptic equations, Elliptic equations on manifolds, general theory, Nonlinear spectral theory, nonlinear eigenvalue problems, Estimates of eigenvalues in context of PDEs, weighted \(p\)-Laplacian, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, gradient estimates, Quasilinear elliptic equations with \(p\)-Laplacian, Dirichlet eigenvalues

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Access URL: https://zbmath.org/7989691
https://doi.org/10.3934/dcdss.2024095

Nonlinear Subwavelength Resonances in Three Dimensions: Nonlinear subwavelength resonances in three dimensions

Authors: Habib Ammari, Thea Kosche

Source: Studies in Applied Mathematics, 154 (3)

Subject Terms: Wave scattering in solid mechanics, Semilinear elliptic equations, capacitance matrix formalism, cubic nonlinear Helmholtz equation, nonlinearity-induced eigenmode, nonlinear subwavelength physics, nonlinear subwavelength resonance, FOS: Physical sciences, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, Mathematical Physics (math-ph), 35P30, 35C20, 74J20, Asymptotic expansions of solutions to PDEs, Resonance in context of PDEs, Mathematical Physics

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Access URL: http://arxiv.org/abs/2410.21173
https://zbmath.org/8023770
https://doi.org/10.1111/sapm.70036
http://hdl.handle.net/20.500.11850/728224

The Existence and Multiplicity of Normalized Solutions for Kirchhoff Equations in Defocusing Case: The existence and multiplicity of normalized solutions for Kirchhoff equations in defocusing case

Authors: Xu, Lin

Source: Analysis in Theory and Applications. 40:191-207

Subject Terms: Integro-partial differential equations, Second-order elliptic systems, Semilinear elliptic equations, Kirchhoff-type equation, Entire solutions to PDEs, mixed nonlinearity, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, normalized solutions

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Access URL: https://zbmath.org/7959285
https://doi.org/10.4208/ata.oa-2023-0027

A novel method for solving the inverse spectral problem with incomplete data

Authors: Pinchao Meng, Zhaobin Xu, Xianchao Wang, Weishi Yin, Hongyu Liu

Source: Journal of Computational and Applied Mathematics. 463:116525

Subject Terms: incomplete data, Boundary value problems for second-order elliptic equations, Scattering theory for PDEs, data-driven, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, inverse spectral problem, Dirichlet-Laplacian eigenvalue, data-driven deep neural network, Artificial neural networks and deep learning

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Some qualitative and quantitative properties of weak solutions to mixed anisotropic and nonlocal quasilinear elliptic and doubly nonlinear parabolic equations

Authors: Garain, Prashanta

Source: Nonlinear Analysis. 256:113796

Subject Terms: pointwise behavior, Quasilinear parabolic equations, regularity, PDEs of mixed type, energy estimates, Smoothness and regularity of solutions to PDEs, existence, Comparison principles in context of PDEs, system of mixed singular equations, semicontinuity, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, A priori estimates in context of PDEs, Fractional partial differential equations, Maximum principles in context of PDEs, 35A01, 35B45, 35B50, 35B51, 35B65, 35J62, 35K59, 35M10, 35P30, 35R11, Mathematics - Analysis of PDEs, Quasilinear elliptic equations, elliptic and doubly nonlinear parabolic mixed anisotropic and nonlocal quasilinear equation, FOS: Mathematics, weak Harnack inequality, De Giorgi theory, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2407.17928

Capacitary inradius and Poincaré-Sobolev inequalities

Authors: Bozzola F., Brasco L.

Source: ESAIM: Control, Optimisation and Calculus of Variations. 31:26

Subject Terms: capacity, inradius, Estimates of eigenvalues in context of PDEs, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, Cheeger's constant, Functional Analysis (math.FA), Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, Boundary value problems for second-order elliptic equations, Poincaré inequality, FOS: Mathematics, Poincaré inequality / inradius / capacity / Cheeger's constant, Quasilinear elliptic equations with \(p\)-Laplacian, Other generalizations (nonlinear potential theory, etc.), Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2405.19786
https://hdl.handle.net/11392/2589390
https://doi.org/10.1051/cocv/2025016
https://www.esaim-cocv.org/articles/cocv/abs/2025/01/cocv240127/cocv240127.html

A Priori Error Analysis of Linear and Nonlinear Periodic Schrödinger Equations with Analytic Potentials: A priori error analysis of linear and nonlinear periodic Schrödinger equations with analytic potentials

Authors: Cancès, Eric, Kemlin, Gaspard, Levitt, Antoine

Contributors: Kemlin, Gaspard

Source: Journal of Scientific Computing. 98

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, Numerical methods for eigenvalue problems for boundary value problems involving PDEs, eigenvalue problems, NLS equations (nonlinear Schrödinger equations), planewave discretization, Analyticity in context of PDEs, Schrödinger equation, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, Numerical Analysis (math.NA), [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Nonlinear elliptic equations, Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, 01 natural sciences, Blow-up in context of PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, Stability in context of PDEs, PDEs in connection with statistical mechanics, Computational density functional analysis in statistical mechanics

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Access URL: http://arxiv.org/abs/2206.04954
https://inria.hal.science/hal-03692851v3/document
https://inria.hal.science/hal-03692851v3
https://doi.org/10.1007/s10915-023-02421-0

On Construction of a Super Hierarchy of the Wadati-Konno-Ichikawa Equation: On construction of a super hierarchy of the Wadati-Konno-Ichikawa equation

Authors: Xuemei Li, Lutong Li

Source: Advances in Mathematical Physics, Vol 2020 (2020)

Subject Terms: Eigenvalues, singular values, and eigenvectors, Physics, QC1-999, NLS equations (nonlinear Schrödinger equations), 0103 physical sciences, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, Rods (beams, columns, shafts, arches, rings, etc.), 0101 mathematics, 16. Peace & justice, 01 natural sciences, 3. Good health

File Description: application/xml; text/xhtml

Access URL: https://downloads.hindawi.com/journals/amp/2020/6838731.pdf
https://doaj.org/article/b00ad2233b9042b386b8e508d1abae43
https://www.hindawi.com/journals/amp/2020/6838731/
https://ideas.repec.org/a/hin/jnlamp/6838731.html
https://downloads.hindawi.com/journals/amp/2020/6838731.pdf
http://downloads.hindawi.com/journals/amp/2020/6838731.pdf

A dynamic $p$-Laplacian: A dynamic \(p\)-Laplacian

Authors: de Diego Unanue, Alvaro, Froyland, Gary, Junge, Oliver, Koltai, Péter

Subject Terms: Nonautonomous smooth dynamical systems, dynamic Cheeger inequality, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, Dynamical Systems (math.DS), \(p\)-Laplacian, Approximation methods and numerical treatment of dynamical systems, Mathematics - Analysis of PDEs, Variational methods involving nonlinear operators, Dynamical systems involving smooth mappings and diffeomorphisms, FOS: Mathematics, dynamic Laplacian, Mathematics - Dynamical Systems, Quasilinear elliptic equations with \(p\)-Laplacian, coherent sets, 37C05, 37C60, 37M99, 35J92, 35P30, 47J30, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2308.05947

Quorum-sensing induced transitions between bistable steady-states for a cell-bulk ODE-PDE model with lux intracellular kinetics

Authors: Wesley Ridgway, Michael J. Ward, Brian T. Wetton

Source: Journal of Mathematical Biology. 84

Subject Terms: 0301 basic medicine, Cell biology, 0303 health sciences, Control/observation systems governed by partial differential equations, PDEs in connection with biology, chemistry and other natural sciences, bistable states, Biophysics, cell-bulk coupling, Quorum Sensing, globally coupled eigenvalue problem, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, Green's function, Models, Theoretical, quorum-sensing, 01 natural sciences, Diffusion, Kinetics, 03 medical and health sciences, Population dynamics (general), bulk diffusion, 0101 mathematics, Control/observation systems governed by ordinary differential equations, Singular perturbations in context of PDEs, lux kinetics

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Access URL: https://pubmed.ncbi.nlm.nih.gov/34928406
https://zbmath.org/7458803
https://doi.org/10.1007/s00285-021-01705-z

The application of the intersect index to quasilinear eigenfunction problems

Authors: Dymarsky, Ya.M.

Subject Terms: Nonlinear spectral theory, nonlinear eigenvalue problems, Spectral theory, eigenvalue problems on manifolds, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, eigenfunction, quasilinear eigenfunction problems, intersect index

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Access URL: https://zbmath.org/1641390
http://dspace.nbuv.gov.ua/handle/123456789/169281

An introduction to fractal uncertainty principle

Authors: Semyon Dyatlov

Contributors: Massachusetts Institute of Technology. Department of Mathematics

Source: arXiv

Subject Terms: FOS: Physical sciences, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, Mathematical Physics (math-ph), Uncertainty relations, also entropic, 01 natural sciences, quantum mechanics on fractal sets, uncertainty principle, Mathematics - Analysis of PDEs, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Spectral theory, eigenvalue problems on manifolds, 0101 mathematics, Quantum chaos, Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices, Mathematical Physics, quantum chaos, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/pdf/1903.02599
http://arxiv.org/abs/1903.02599
https://zbmath.org/7102675
https://doi.org/10.1063/1.5094903
https://par.nsf.gov/biblio/10119851-introduction-fractal-uncertainty-principle
https://aip.scitation.org/doi/10.1063/1.5094903
http://ui.adsabs.harvard.edu/abs/2019JMP....60h1505D/abstract
http://export.arxiv.org/pdf/1903.02599
https://arxiv.org/pdf/1903.02599
https://arxiv.org/abs/1903.02599
https://hdl.handle.net/1721.1/136419

Quasilinear Schrödinger equations with nonlinearities interacting with high eigenvalues

Authors: Edcarlos D. Silva, J. S. Silva

Source: Journal of Mathematical Physics. 60

Subject Terms: quasilinear Schrödinger equations, NLS equations (nonlinear Schrödinger equations), eigenvalues, Estimates of eigenvalues in context of PDEs, Existence problems for PDEs: global existence, local existence, non-existence, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, 0101 mathematics, 01 natural sciences

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Access URL: https://zbmath.org/7102674
https://doi.org/10.1063/1.5091810
http://ui.adsabs.harvard.edu/abs/2019JMP....60h1504S/abstract
https://aip.scitation.org/doi/10.1063/1.5091810

A Phase Plane Analysis of the 'Multi-Bubbling' Phenomenon in Some Slightly Supercritical Equations: A phase plane analysis of the ``multi-bubbling'' phenomenon in some slightly supercritical equations

Authors: Del Pino, Manuel, Dolbeault, Jean, Musso, Monica

Source: Nonlinear Differential Equation Models ISBN: 9783709172087

Subject Terms: singular solutions, supercritial problem, Bifurcation theory for ordinary differential equations, branches of solutions, bifurcation diagram, critical and super-critical problems, phase plane analysis, p-Laplacian, spikes, Gelfand problem, Lyapunov-Schmidt reduction, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, dynamical systems, Nonlinear elliptic equations, Analyse, bubbles, Emden-Fowler transform, multi-peaks, supercritical case, Brezis-Nirenberg problem, Singular perturbations in context of PDEs

File Description: application/xml; application/pdf; application/postscript

Access URL: https://zenodo.org/record/45822/files/article.pdf
https://basepub.dauphine.psl.eu/bitstream/123456789/6136/2/2003-24.pdf
https://zbmath.org/2111474
https://doi.org/10.1007/s00605-004-0236-5
http://www.ceremade.dauphine.fr/~dolbeaul/Preprints/Fichiers/Vienna9.pdf
https://www.ceremade.dauphine.fr/~dolbeaul/Preprints/Fichiers/Vienna9.pdf
https://link.springer.com/10.1007/978-3-7091-0609-9_7
https://dialnet.unirioja.es/servlet/articulo?codigo=890432
https://documat.unirioja.es/servlet/articulo?codigo=890432
https://basepub.dauphine.fr/handle/123456789/6136?show=full

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)

File Description: application/xml

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

Superlinear critical resonant problems with small forcing term

Authors: Colette De Coster, Mabel Cuesta

Source: Calculus of Variations and Partial Differential Equations. 54:349-363

Subject Terms: 0211 other engineering and technologies, General topics in linear spectral theory for PDEs, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, 02 engineering and technology, quasilinear elliptic problems, 0101 mathematics, Higher-order elliptic equations, \(p\)-Laplacian, Dirichlet boundary conditions, 01 natural sciences

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007/s00526-014-0788-8/fulltext.html
https://link.springer.com/article/10.1007/s00526-014-0788-8

An eigenvalue problem for a quasilinear elliptic field equation: An eigenvalue problem for a quasilinear elliptic field equation.

Authors: Visetti, Daniela

Source: Nonlinear Analysis: Theory, Methods & Applications. 47:5991-5997

Subject Terms: Variational methods involving nonlinear operators, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, Nonlinear elliptic equations, 0101 mathematics, 01 natural sciences, Singular perturbations in context of PDEs

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/pii/S0362546X01006952
https://hdl.handle.net/11572/47772
http://cos.fit.edu/math/ifna/wcna/wcna2000.htm
https://hdl.handle.net/11572/90442