We study boundary-value problems of the type
where p>1, , and is positive. We provide multiplicity results when f behaves like a cubic with three distinct roots, at which it satisfies Lipschitz-type conditions involving a parameter q>1. We shall show how changes in the position of q with respect to p lead to different behavior of the solution set. When dealing with sign-changing solutions, we assume that f is half-odd; a condition generalizing the usual oddness. We use a quadrature method.
Submitted April 16, 1999. Revised May 1, 2000. Published July 3, 2000.
Math Subject Classifications: 34B15.
Key Words: p-Laplacian, time-maps, multiplicity results, cubic-like nonlinearities.
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| Idris Addou |
USTHB, Institut de Mathematiques
El-Alia, B.P. no. 32 Bab-Ezzouar
16111, Alger, Algerie.
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