Nonlocal elliptic problems with nonhomogeneous nonlinearities via nonlinear Rayleigh quotient in

Abstract

It is established ground states and multiplicity of solutions for a nonlocal Schrödinger equation in , , where , and , under general conditions over the measurable functions a, b, V and f. The nonlinearity f is superlinear at infinity and at the origin, and does not satisfy any Ambrosetti-Rabinowitz type condition. It is considered that the weights a and b are not necessarily bounded and the potential V can change sign. We obtained a sharp ⁎ which guarantees the existence of at least two nontrivial solutions for each ⁎. Our approach is variational in its nature and is based on the nonlinear Rayleigh quotient method together with some fine estimates. Compactness of the problem is also considered.