A uniqueness theorem for two-point boundary value problems

Abstract

We prove a uniqueness theorem for solutions of two-point boundary value problems, which says that when the nonlinearity is sublinear and Lipschitzian, and one of the boundary values is fixed, then for sufficiently large values of the other boundary value there is a unique solution of the problem. The proof is based on the Banach's fixed-point theorem, and the argument used to show that the relevant operator is a contraction makes use of a generalization of the Riemann-Lebesgue lemma

Keywords:

• Two-point boundary value problem
• uniqueness
• reaction-diffusion equation
• Banach fixed point theorem
• weak convergence