On Nonhomogeneous Biharmonic Equations Involving Critical Sobolev Exponent

M. Guedda

Abstract: In this paper we consider the problem $\Delta^2 u=\lambda\,|u|^{q_c-2}\,u+f$ in $\Omega$, $u=\Delta u=0$ on $\partial\Omega$, where ${q_c}=2N/(N-4)$, $N>4$, is the limiting Sobolev exponent and $\Omega$ is a smooth bounded domain in ${\R}^N$. Under some restrictions on $f$ and $\lambda$, the existence of weak solution $u$ is proved. Moreover $u\geq0$ for $f\geq 0$ whenever $\lambda\geq 0$.

Classification (MSC2000): 35J65, 35J20, 49J45.

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