MATHEMATICA BOHEMICA, Vol. 121, No. 1, pp. 41-54, 1996

Two solutions for a nonlinear Dirichlet problem with positive forcing

J. Matos, L. Sanchez

J. Matos, L. Sanchez, Universidade de Lisboa, Centro de Matematica e Aplicac oes Fundamentais, Avenida Professor Gama Pinto, 2, 1699 - Lisboa Codex, Portugal

Abstract: Given a semilinear elliptic boundary value problem having the zero solution and where the nonlinearity crosses the first eigenvalue, we perturb it by a positive forcing term; we show the existence of two solutions under certain conditions that can be weakened in the onedimensional case.

Keywords: semilinear elliptic equations, multiple solutions, shooting method, variational methods

Classification (MSC91): 34B15, 35J25

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