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2003 Sharp solvability conditions for a fourth-order equation with perturbation
Frédéric Robert, Kunnath Sandeep
Differential Integral Equations 16(10): 1181-1214 (2003).

Abstract

Let $B$ be the unit ball of ${\mathbb{R}^n}$, $n\geq 5$, and $\rho:\mathbb{R}\rightarrow\mathbb{R}$ a smooth function. We consider the following critical problem: $$\left\{\begin{array}{ll} \Delta^2 u=|u|^{\frac{8}{n-4}}u+\rho(u) & \hbox{ in }B\\ u\not\equiv 0 & \\ u=\frac{\partial u}{\partial n}=0 & \hbox{ on }\partial B . \end{array}\right.$$ We give sufficient conditions for the existence of solutions to this problem. These conditions are close to being sharp, as we prove by considering the problem on arbitrary small balls.

Citation

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Frédéric Robert. Kunnath Sandeep. "Sharp solvability conditions for a fourth-order equation with perturbation." Differential Integral Equations 16 (10) 1181 - 1214, 2003.

Information

Published: 2003
First available in Project Euclid: 21 December 2012

zbMATH: 1145.35334
MathSciNet: MR2014806

Subjects:
Primary: 35J40
Secondary: 35J60

Rights: Copyright © 2003 Khayyam Publishing, Inc.

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Vol.16 • No. 10 • 2003
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