Positive solution for a nonlocal problem with strong singular nonlinearity

Abstract

In this article, we consider a nonlocal problem with a strong singular term and a general weight function. By using Ekeland’s variational principle, we prove a necessary and sufficient condition for the existence of a positive solution. Moreover, a method of algebraic analysis is used to deal with the multiplicity of solutions. Compared with the existing literature, our problems and results are novel.

Keywords

• nonlocal problem
• strong singular term
• ekeland’s variational principle
• algebraic analysis
• positive solution
• 35b09
• 35j75
• 35j60