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august 2013 Multiplicity of solutions for a biharmonic equation with subcritical or critical growth
Giovany M. Figueiredo, Marcos T. O. Pimenta
Bull. Belg. Math. Soc. Simon Stevin 20(3): 519-534 (august 2013). DOI: 10.36045/bbms/1378314513

Abstract

We consider the fourth-order problem $$ \left\{ \begin{array}{l} \epsilon^4\Delta^2u + V(x)u = f(u) + \gamma|u|^{2_{**}-2}u \mbox{in $\mathbb{R}^N$}\\ u\in H^2(\mathbb{R}^N), \end{array} \right. $$ where $\epsilon > 0$, $N\geq 5$, $V$ is a positive continuous potential, $f$ is a function with subcritical growth and $\gamma \in \{0,1\}$. We relate the number of solutions with the topology of the set where $V$ attain its minimum values. We consider the subcritical case $\gamma=0$ and the critical case $\gamma=1$. In the proofs we apply Ljusternik-Schnirelmann theory.

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Giovany M. Figueiredo. Marcos T. O. Pimenta. "Multiplicity of solutions for a biharmonic equation with subcritical or critical growth." Bull. Belg. Math. Soc. Simon Stevin 20 (3) 519 - 534, august 2013. https://doi.org/10.36045/bbms/1378314513

Information

Published: august 2013
First available in Project Euclid: 4 September 2013

zbMATH: 1282.35152
MathSciNet: MR3129056
Digital Object Identifier: 10.36045/bbms/1378314513

Subjects:
Primary: 35J30
Secondary: 35J35

Keywords: biharmonic equations , nontrivial solutions , variational methods

Rights: Copyright © 2013 The Belgian Mathematical Society

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Vol.20 • No. 3 • august 2013
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