Concentration of positive ground state solutions for critical Kirchhoff equation with competing potentials

2020/07/27 by Yongpeng Chen, Chen, Yongpeng, Zhipeng Yang +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2007.13827

openalex publication_date 2020/07/27 · openalex created_date 2020/08/03 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the following singularly perturbed Kirchhoff equation -(ε²a+ε b∫_ℝ³|∇ u|²dx)Δu+V(x)u=P(x)|u|^p-2u+Q(x)|u|⁴u, x∈ℝ³, where ε>0 is a small parameter, a, b > 0 are constants, p∈(4,6) and V, P, Q are potential functions satisfying some competing conditions. We prove the existence of a positive ground state solution by using variational methods, and we determine a concrete set related to the potentials V,P and Q as the concentration position of these ground state solutions as ε→0.

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