Existence of infinitely many solutions for semilinear degenerate Schrodinger equations

In this paper, we study the existence of infinitely many nontrivial solutions of to the semilinear A.,. differential equations in RN {-Delta(gamma)u+ b(x)u = f (x, u) m R-N, u is an element of S-gamma(2)(R-N), where Delta(gamma) is a subelliptic operator, the potential b(x) and nonlinearity f(x, u) are not assumed to be continuous. Multiplicity of nontrivial solutions for semilinear Laplace equations in R-N with continuous potential and nonlinearity was considered in many works, such as [4,15,18,24]. (C) 2018 Elsevier Inc. All rights reserved.