Academic Journal
Perturbation Effects for Anisotropic Non-Autonomous Kirchhoff–Schrödinger Equations With Exponential Growth.
| Τίτλος: | Perturbation Effects for Anisotropic Non-Autonomous Kirchhoff–Schrödinger Equations With Exponential Growth. |
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| Συγγραφείς: | Ahmad, Bashir, Nyamoradi, Nemat, Van Thin, Nguyen |
| Πηγή: | Asymptotic Analysis; Sep2026, Vol. 149 Issue 3, p1151-1181, 31p |
| Θεματικοί όροι: | Variational approach (Mathematics), Fractional differential equations, Nonlinear theories, Autonomous differential equations, Partial differential equations, Laplacian operator |
| Περίληψη: | In this article, we study the existence of solutions to a non-autonomous anisotropic fractional equation M ([ v ] s , p p) (− Δ) N s s v + ∑ i = 1 m M i ([ v ] s , p i p i ) (− Δ) p i s v + V (ε x) (| v | N s − 2 v + ∑ i = 1 m | v | p i − 2 v) = Q (ε x) f (v) in R N , where ε is a positive parameter, m ≥ 1 , N = p s , s ∈ (0 , 1) and 2 ≤ (N / s) = p < p 1 < ⋯ < p m. Further, the nonlinear function f exhibits critical as well as supercritical exponential growth, while absorption potential V and reaction potential Q are bounded continuous functions, M (t) = a + b t , a > 0 , b > 0 and M i (t) = a i + b i t , a i > 0 , b i > 0 , i = 1 , ... , m are Kirchhoff functions. By applying variational methods, we prove the existence of a nontrivial nonnegative solution to the given equation when ε is small enough. [ABSTRACT FROM AUTHOR] |
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| Βάση Δεδομένων: | Complementary Index |
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