Existence of solutions for a quasilinear problem with fast nonlocal terms

Abstract

In this paper, it is considered the existence of a solution for a nonlocal equation involving the p-Laplacian operator which is related to several applications such as vibration problems, flow of fluids through a homogeneous isotropic rigid porous medium, nuclear reactor's dynamics and in population dynamics. The approach is based on sub-supersolution arguments and Schauder's fixed point theorem. An important fact is that our result is valid for nonlocal terms which may exhibit a growth higher than p.

Keywords:

• p-Laplacian
• nonlocal problem
• fixed point
• quasilinear equation
• sub-supersolutions

2020 Mathematics Subject Classification:

• 35A16

Acknowledgments

The authors would like to thank the comments of the referees which improved the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.