Existence and uniqueness of weak and classical solutions for a fourth-order semilinear boundary value problem

Abstract

This paper is concerned with the problem of existence and uniqueness of weak and classical solutions for a fourth-order semilinear boundary value problem. The existence and uniqueness for weak solutions follows from standard variational methods, while similar uniqueness results for classical solutions are derived using maximum principles.
 
 
 
 
 
 
 doi:10.1017/S1446181119000129

The study of a fourth-order differential equation: existence, uniqueness and a dynamical system approach

“…For further uniqueness results (in higher dimensions) the reader is referred to the paper [7] and [8].…”