Existence and multiplicity of solutions for Schrödinger equations with sublinear nonlinearities

Abstract

In the paper, we investigate a class of Schrödinger equations with sign-changing potentials V(x) and sublinear nonlinearities. We remove the coercive condition on V(x) usually required in the existing literature and also weaken the conditions on nonlinearities. By proving a Hardy-type inequality, extending the results in [1], and using it together with variational methods, we get at least one or infinitely many small energy solutions for the problem.

Keywords

• schrödinger equation
• sublinear nonlinearity
• hardy-type inequality
• variant fountain theorem
• infinitely many solutions