A fourth-order equation with critical growth: the effect of the domain topology
DOI:
https://doi.org/10.12775/TMNA.2015.026Keywords
Biharmonic equation, Critical exponent, Lusternik-Schnirelman category, Positive solutions.Abstract
In this paper we prove the existence of multiple classical solutions for the fourth-order problemwhere $\Omega$ is a smooth bounded domain in $\rn$, $N\geq8$, $2_*=2N/(N-4)$ and $\mu_1(\Omega)$ is the first eigenvalue of $\Delta^2$ in $H^2(\Omega)\cap H_{0}^{1}(\Omega)$. We prove that there exists $0<\overline{\mu}<\mu_1(\Omega)$ such that, for each $0<\mu<\overline{\mu}$, the problem has at least $\cat_{\Omega}(\Omega)$ solutions.
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Published
2015-06-01
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MELO, Jessyca Lange Fereira and DOS SANTOS, Ederson Moreira. A fourth-order equation with critical growth: the effect of the domain topology. Topological Methods in Nonlinear Analysis. Online. 1 June 2015. Vol. 45, no. 2, pp. 551 - 574. [Accessed 29 March 2024]. DOI 10.12775/TMNA.2015.026.
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