Positive solutions for semilinear elliptic problem with nonlinear boundary condition on conical Sobolev spaces

Koozehgar   Kalleji, Morteza

doi:10.22055/jamm.2024.47076.2278

Positive solutions for semilinear elliptic problem with nonlinear boundary condition on conical Sobolev spaces

Document Type : Original Paper

Author

Morteza Koozehgar Kalleji

Department of Mathematics, Faculty of Sciences Arak University, Arak, 38156-8-8349, Iran

10.22055/jamm.2024.47076.2278

Abstract

In this paper, a system of elliptic equations with a perturbation in the system and also the nonlinear Neumann boundary conditions near a conical singular point are studied. By introducing the conical Sobolv space and using variational methods and Nehari manifold method, we will prove the existence of at least two positive solutions for this problem on the conical Sobolev space.

Keywords