Existence of the Solution to Semilinear Biharmonic Equation

Abstract

A class of semilinear bihaxmonic problem in a bounded convex domainΩR~d,d = 2,3,is considered.The nonlinear termφ(|▽u|) grows with |▽u|~p.In terms of Schaefer's fixed pointtheorem,as d = 2(or d = 3) and p satisfies 2≤p +∞(or 2≤p≤6),the solution exists and islocal uniqueness.