A new existence result for some nonlocal problems involving Orlicz spaces and its applications

Abstract

Abstract This paper studies some quasilinear elliptic nonlocal equations involving Orlicz–Sobolev spaces. On the one hand, a new sub-supersolution theorem is proved via the pseudomonotone operator theory; on the other hand, using the obtained theorem, we present an existence result on the positive solutions of a singular elliptic nonlocal equation. Our work improves the results of some previous researches.

Keywords

• Orlicz–Sobolev space
• Sub-supersolution
• Pseudomonotone Operator Theorem
• Luxemburg norm
• Φ-Laplace operator