On a complete parametric Sturm-Liouville problem with sign changing coefficients

Abstract

In this paper we study a complete second order differential equation of Sturm-Liouville type under Dirichlet boundary condition and where the variable coefficients are allowed to be sign changing. Through critical point theory, we obtain the existence of two nontrivial generalized solutions by requiring a specific growth on the nonlinearity. Moreover, the solutions turn out to be nonnegative and with opposite energy sign.

Keywords

• critical point theory
• sturm-liouville equations
• nonlinear differential problems
• ordinary differential equations
• multiple results