Electron. J. Diff. Eqns., Vol. 2000(2000), No. 18, pp. 1-9.

Minimax principles for critical-point theory in applications to quasilinear boundary-value problems

A. R. El Amrouss & M. Moussaoui

Using the variational method developed by the same author in [7], we establish the existence of solutions to the equation $-\Delta_p u = f(x,u)$ with Dirichlet boundary conditions. Here $\Delta_p$ denotes the p-Laplacian and $\int_0^s f(x,t)\,dt$ is assumed to lie between the first two eigenvalues of the p-Laplacian.

Submitted September 9, 1999. Published March 8, 2000.
Math Subject Classifications: 49J35, 35J65, 35B34.
Key Words: Minimax methods, p-Laplacian, resonance.

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A. R. El Amrouss & M. Moussaoui
University Mohamed I
Faculty of sciences
Department of Mathematics
Oujda, Moroco
e-mail: amrouss@sciences.univ-oujda.ac.ma
e-mail: moussaoui@sciences.univ-oujda.ac.ma

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