Multiplicity for a strongly singular quasilinear problem via bifurcation theory

Abstract

A [Formula: see text]-Laplacian elliptic problem in the presence of both strongly singular and [Formula: see text]-superlinear nonlinearities is considered. We employ bifurcation theory, approximation techniques and sub-supersolution method to establish the existence of an unbounded branch of positive solutions, which is bounded in positive [Formula: see text]-direction and bifurcates from infinity at [Formula: see text]. As consequence of the bifurcation result, we determine intervals of existence, nonexistence and in particular cases, global multiplicity.

Keywords

• Strongly singular nonlinearities
• -superlinear terms
• bifurcation theory
• comparison principle for -sub and supersolutions