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

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.

• nonlocal elliptic problems
• positive solutions
• existence of solutions
• uniqueness of solutions
• parameter dependencies
• positive radial solutions
• one-dimensional problems
• multidimensional problems
• fixed point theorems
• reaction term
• diffusion coefficient

• Nonlinear Differential Equations Analysis
• Nonlinear Partial Differential Equations
• Differential Equations and Boundary Problems
• nonlocal elliptic problems
• positive solutions
• existence of solutions
• uniqueness of solutions
• parameter dependencies
• positive radial solutions
• one-dimensional problems
• multidimensional problems
• Applied Mathematics
• Mathematics