Uniqueness of nonnegative solutions for semipositone problems on exterior domains

Uniqueness and Stability of Nonnegative Solutions for Semipositone Problems in a Ball

We study the uniqueness and stability of nonnegative solutions for classes of nonlinear elliptic Dirichlet problems on a ball, when the nonlinearity is monotone, negative at the origin, and either concave or convex.

Uniqueness and Nonexistence of Positive Solutions to Semipositone Problems

We consider the uniqueness of the positive solution to a semilinear elliptic equation with Dirichlet boundary condition and the nonlinearity satisfying f(0) < 0 and having asymptotic sublinear growth rate. A similar idea is also applied to the nonexistence of a positive solution to a superlinear problem.

On the existence of nonnegative solutions for a class of fractional boundary value problems

‎In this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎By applying Kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary BVP formulated by truncating the response function‎. ‎Then the Arzela--Ascoli theorem is used to take $C^1$ ...

Multiple Positive Solutions of Semilinear Elliptic Problems in Exterior Domains

Existence and uniqueness of the scattering solutions in the exterior of rough domains

A simple and short proof is given for the existence and uniqueness of the solution to the obstacle scattering problem under weak smoothness assumptions on the obstacle. The Robin, Neumann and Dirichlet boundary conditions are considered.