Multiplicity of negative-energy solutions for singular-superlinear Schrödinger equations with indefinite-sign potential

We are concerned with the multiplicity of positive solutions for singular superlinear and subcritical Schrödinger equation [Formula: see text] beyond Nehari extremal value, as defined in [Y. Il’yasov, On extreme values manifold via nonlinear Rayleigh’s quotient, Topol. Methods Nonlinear Anal. 49 (2017) 683–714], when potential may change its sign, text], is a continuous function, real parameter. The main difficulties come from non-differentiability energy functional fact that intersection boundaries connected components set non-empty. overcome these by exploring topological structures boundary to build non-empty sets whose have empty minimizing over them controlling level.