Existence of positive solutions for double-phase problem

Abstract

In this work, we discuss the existence of positive solutions of a class of differential equations called double phase with Dirichlet condition, that involves both a singular and a superlinear parametric term, posed by the discontinuous weights and the the structure of the differential operator. Using Nehari’s method and critical point theory, it is shown that for small values of the argument of the parameter λ, the equation admits at least two positive solutions.