The existence of positive solutions for Kirchhoff-type problems via the sub-supersolution method

Abstract

In this paper we discuss the existence of a solution between wellordered subsolution and supersolution of the Kirchhoff equation. Using the sub-supersolution method together with a Rabinowitz-type global bifurcation theory, we establish the existence of positive solutions for Kirchhoff-type problems when the nonlinearity is singular or sign-changing. Moreover, we obtain some necessary and sufficient conditions for the existence of positive solutions for the problem when N = 1.

Keywords

• kirchhoff-type elliptic problems
• rabinowitz-type global bifurcation theory
• sub-supersolution method
• existence
• uniqueness
• 35j60
• 35j75
• 47h10