Multiplicity and concentration of solutions for Kirchhoff equations with exponential growth
| Autor: | Xueqi Sun, Yongqiang Fu, Sihua Liang |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Bulletin of Mathematical Sciences, Vol 14, Iss 03 (2024) |
| Druh dokumentu: | article |
| ISSN: | 16643607 1664-3615 1664-3607 |
| DOI: | 10.1142/S1664360724500048 |
| Popis: | In this paper, we deal with fractional [Formula: see text]-Laplace Kirchhoff equations with exponential growth of the form 𝜀ps(a + b[u] s,pp)(−Δ) psu + Z(x)|u|p−2u = h(u)in ℝN, where [Formula: see text] is a positive parameter, [Formula: see text], [Formula: see text] and [Formula: see text]. Under some appropriate conditions for the nonlinear function [Formula: see text] and potential function [Formula: see text], and with the help of penalization method and Lyusternik–Schnirelmann theory, we establish the existence, multiplicity and concentration of solutions. To some extent, we fill in the gaps in [W. Chen and H. Pan, Multiplicity and concentration of solutions for a fractional [Formula: see text]-Kirchhoff type equation, Discrete Contin. Dyn. Syst. 43 (2023) 2576–2607; G. Figueiredo and J. Santos, Multiplicity and concentration behavior of positive solutions for a Schrödinger–Kirchhoff type problem via penalization method, ESAIM Control Optim. Calc. Var. 20 (2014) 389–415; X. He and W. Zou, Existence and concentration behavior of positive solutions for a Kirchhoff equation in [Formula: see text] J. Differential Equations 252 (2012) 1813–1834; J. Wang, L. Tian, J. Xu and F. Zhang, Multiplicity and concentration of positive solutions for a Kirchhoff type problem with critical growth, J. Differential Equations 253 (2012) 2314–2351]. |
| Databáze: | Directory of Open Access Journals |
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