Existence of solution for a class of indefinite variational problems with discontinuous nonlinearity

2020/12/07 by Claudianor O. Alves, Alves, Claudianor O., Geovany F. Patricio +1
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2012.03641

Abstract

This paper concerns the existence of a nontrivial solution for the following problem \\beginaligned -Δu + V(x)u amp; ∈ ∂_u F(x,u) a.e. in ℝ^N,u ∈ H¹(ℝ^N). \endaligned .\leqno(P) where F(x,t)=∫₀^tf(x,s) ds, f is a ℤ^N-periodic Caratheodory function and λ=0 does not belong to the spectrum of -Δ+V. Here, ∂_t F denotes the generalized gradient of F with respect to variable t.

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