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(2000 / vol.3 / no.1)
Nontrivial Solutions of a Nonlinear Biharmonic Equation
Q-Heung Choi, Tacksun Jung
Pages. 35-42     



Let $Omega$ be a smooth bounded region in $R^n$ with smooth
boundary $partial Omega$. We study the multiplicity of solutions
of the nonlinear biharmonic equation with Dirichlet boundary
condition, $Delta^2 u + c Delta u = g(u)$ in $Omega$, where $c
in R$ and $Delta^2$ denote the biharmonic operator. We show that
the equation has nontrivial solutions when $g : R
ightarrow R$
is a differentiable function tith some condition such that $g(0) =
0$.



1. Introduction 2. A Variational Reduction Method 3. A Degree Theory Applied to P.D.E. 4. Proof of The Main Results



Multiple solutions, biharmonic equation, variational reduction method, degree theory



35J40