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Multiplicity and concentration of solutions for Kirchhoff equations with exponential growth

    https://doi.org/10.1142/S1664360724500048Cited by:7 (Source: Crossref)

    In this paper, we deal with fractional pp-Laplace Kirchhoff equations with exponential growth of the form

    𝜀ps(a+b[u]ps,p)(Δ)spu+Z(x)|u|p2u=h(u)in N,
    where 𝜀 is a positive parameter, a,b>0, s(0,1) and p=Ns2. Under some appropriate conditions for the nonlinear function h and potential function Z, 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 p-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 3,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].

    Communicated by Vicentiu Radulescu

    AMSC: 35A15, 35A23, 35J35, 35J60, 35R11