Ground state solution for a class of indefinite variational problems with critical growth

2017/04/05 by Claudianor O. Alves, Alves, Claudianor O., Geilson F. Germano +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1704.01385

arxiv created 2017/04/05 · openalex publication_date 2017/04/05 · arxiv updated 2017/04/06 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In this paper we study the existence of ground state solution for an indefinite variational problem of the type \-Δu+(V(x)-W(x))u=f(x,u) in \R^N, u∈ H¹(\R^N),. \eqno(P) where N ≥ 2, V,W:ℝ^N → ℝ and f:ℝ^N × ℝ → ℝ are continuous functions verifying some technical conditions and f possesses a critical growth. Here, we will consider the case where the problem is asymptotically periodic, that is, V is ℤ^N-periodic, W goes to 0 at infinity and f is asymptotically periodic.

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