Nonlinear Schrödinger equations with concave-convex nonlinearities.

This paper aims to investigate the existence and multiplicity of stationary solutions to the nonlinear Schrödinger equation with concave-convex nonlinearities. The main contribution of this research lies in the fact that zero lies in the boundary of the spectrum of the strongly indefinite Schrödinger operator. Our approach utilizes a novel perturbing method, specifically designed for cases where zero is situated within the spectral gap of the Schrödinger operator. By applying a generalized linking argument concerning the strongly indefinite functional, we establish the existence of two sequences of solutions to the perturbing equation, each corresponding to positive and negative energy states respectively. Finally, we employ the perturbing method to demonstrate the existence of two solutions to our equation. [ABSTRACT FROM AUTHOR]