Solutions to nonlinear elliptic equations with a nonlocal boundary condition

Abstract

We study an elliptic equation and its evolution problem on a bounded domain with nonlocal boundary conditions. Eigenvalue problems, existence, and dynamic behavior of solutions for linear and semilinear equations are investigated. We use the comparison principle and a semigroup approach.

Keywords

• nonlocal boundary condition
• eigenvalue
• comparison principle
• semigroup.