Existence and uniqueness of positive solution to a new class of nonlocal elliptic problem with parameter dependency

Abstract

Abstract In this paper, we prove that under weak assumptions on the reaction terms and diffusion coefficients, a positive solution exists for a one-dimensional case and a positive radial solution to a multidimensional case of a nonlocal elliptic problem. Additionally, we establish the uniqueness of the solution, with the fixed point theorem being the primary tool employed. Our results are new and generalize several existing results.

Keywords

• Existence
• Nonlocal elliptic problem
• Diffusion coefficient
• Fixed point theorem
• Reaction term
• Nonlinear equations