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Electronic Journal of Differential Equations USA-Chile Workshop on Nonlinear Analysis,
Electron. J. Diff. Eqns., Conf. 06, 2001, pp. 243-255.

On a fourth order superlinear elliptic problem

M. Ramos & P. Rodrigues

Abstract:
We prove the existence of a nonzero solution for the fourth order elliptic equation
$$\Delta^2u= \mu u +a(x)g(u)$$
with boundary conditions $u=\Delta u=0$. Here, $\mu$ is a real parameter, $g$ is superlinear both at zero and infinity and $a(x)$ changes sign in $\Omega$. The proof uses a variational argument based on the argument by Bahri-Lions [3].

Published January 1, 2001.
Math Subject Classifications: 35J25, 35J20, 58E05.
Key Words: Superlinear elliptic problems, Morse index, biharmonic operator.

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Miguel Ramos
CMAF, Universidade de Lisboa
Av. Prof. Gama Pinto, 2
1649-003 Lisboa, Portugal
e-mail: mramos@lmc.fc.ul.pt

Paula Rodrigues
FCT, Universidade Nova de Lisboa
Quinta da Torre
2825 Monte da Caparica, Portugal
e-mail: paula.p.rodrigues@netc.pt


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