Existence and multiplicity of positive solutions for a class of Kirchhoff type problems with singularity and critical exponents

Abstract

In this paper, we study the multiplicity results of positive solutions for a class of Kirchhoff type problems with singularity and critical exponents. Combining with the Nehari method and variational method, we prove the existence of positive ground state solutions. Furthermore, we obtain a relationship between the number of positive solutions and the topology of the global maximum set of Q(x).

Keywords

• multiple positive solutions
• critical exponents
• singularity
• nehari method
• variational method