Multi-bump solutions for a Kirchhoff problem type

2015/07/27 by Claudianor O. Alves, Alves, Claudianor O., Giovany M. Figueiredo +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1507.07361

openalex publication_date 2015/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we are going to study the existence of solution for the following Kirchhoff problem \ M\biggl(∫_ℝ³|∇ u|² dx +∫_ℝ³ λa(x)+1)u² dx\biggl) \biggl(- Δu + (λa(x)+1)u\biggl) = f(u) in ℝ³,

u ∈ H¹(ℝ³). . Assuming that the nonnegative function a(x) has a potential well with int (a^-1(\0\)) consisting of k disjoint components Ω₁, Ω₂, ....., Ω_k and the nonlinearity f(t) has a subcritical growth, we are able to establish the existence of positive multi-bump solutions by variational methods.

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