Existence of infinitely many solutions for semilinear degenerate Schrödinger equations

In this paper, we study the existence of infinitely many nontrivial solutions of to the semilinear Δγ differential equations in RN{−Δγu+b(x)u=f(x,u) in RN,u∈Sγ2(RN), where Δγ 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 RN with continuous potential and nonlinearity was considered in many works, such as [4], [15], [18], [24].