Existence of solution for a class of elliptic equation with\n discontinuous nonlinearity and asymptotically linear

2020/12/13 by Claudianor O. Alves, Alves, Claudianor O., Geovany F. Patricio +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2012.07031

openalex publication_date 2020/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper concerns the existence of a nontrivial solution for the following\nproblem\n n
left

beginaligned\n -
Delta u + V(x)u amp;
in
partial_u F(x,u)
;
;
mboxa.e.\nin
;
;
mathbbR^N,
nonumber\n u
in H¹(
mathbbR^N),\n
endaligned\n
right.
leqno(P)\n where F(x,t)=\∫₀^tf(x,s) ,ds, f is a discontinuous\nfunction and asymptotically linear at infinity, \λ=0 is in a spectral\ngap of -\Δ+V, and \∂_t F denotes the generalized gradient of F\nwith respect to variable t. Here, by employing Variational Methods for\nLocally Lipschitz Functionals, we establish the existence of solution when f\nis periodic and non periodic\n

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