Multiplicity of positive solutions for (p,q)-Laplace equations with two parameters

Abstract

We study the zero Dirichlet problem for the equation [Formula: see text] in a bounded domain [Formula: see text], with [Formula: see text]. We investigate the relation between two critical curves on the [Formula: see text]-plane corresponding to the threshold of existence of special classes of positive solutions. In particular, in certain neighborhoods of the point [Formula: see text], where [Formula: see text] is the first eigenfunction of the [Formula: see text]-Laplacian, we show the existence of two and, which is rather unexpected, three distinct positive solutions, depending on a relation between the exponents [Formula: see text] and [Formula: see text].