Multiple solutions of boundary value problems: an elementary approach via the shooting method |
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| Authors: | Gheorghe Dinca Luis Sanchez |
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| Institution: | 1. Faculty of Mathematics, Bucharest University, Str. Academiei 14, 70109, Bucharest, Romania
2. Centro de Matemática e Aplica??es Fundamentais, Universidade de Lisboa, Avenida Professor Gama Pinto, 2, 1699, Lisboa Codex, Portugal
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| Abstract: | In this paper we derive the existence of multiple solutions for boundary value problems of the type $$u\prime \prime + f\left( {t,u} \right) = 0,u\left( 0 \right) = 0,u\left( \pi \right) = 0$$ , in terms of the behaviour of the ratiof(t,u)/u nearu=0 and near infinity. The nonlinear termf is assumed to be locally Lipschitz inu, so that the shooting method can be used. (AMS Subject Classification: 34B15). |
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