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  Full text of the article: