2014/08/23 by Juntao Sun, Sun, Juntao, Tsung‐fang Wu +2
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #math.AP
paper · pdf · doi:10.48550/arxiv.1408.5502
arxiv created 2014/08/23 · openalex publication_date 2014/08/23 · arxiv updated 2014/08/26 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
The purpose of this paper is to study the indefinite Kirchhoff type problem: \ M( ∫ℝN(|∇ u|2+u2)dx) [ -Δu+u] =f(x,u) · in ℝN,
0≤ u∈ H1( ℝN), · . where N≥ 1, M(t)=am( t) +b, m∈ C(ℝ+) and f(x,u)=g(x,u)+h(x)uq-1. We require that f is \textquotedblleft local\textquotedblright sublinear at the origin and \textquotedblleft local\textquotedblright linear at infinite. Using the mountain pass theorem and Ekeland variational principle, the existence and multiplicity of nontrivial solutions are obtained. In particular, the criterion of existence of three nontrivial solutions is established.