Electron.n. J. Diff. Eqns., Vol. 1999(1999), No. 09, pp. 1-29.

Boundary-value problems for the one-dimensional p-Laplacian with even superlinearity

Idris Addou & Abdelhamid Benmezai

Abstract:
This paper is concerned with a study of the quasilinear problem
$-(|u'|^{p-2}u')'= |u|^p-\lambda$, in (0,1)
$u(0) =u(1) =0$,
where p greater than 1 and $\lambda \in {\Bbb R}$ are parameters. For $\lambda$ positive, we determine a lower bound for the number of solutions and establish their nodal properties. For $\lambda \leq 0$, we determine the exact number of solutions. In both cases we use a quadrature method.

Submitted October 28, 1998. Published March 8, 1999.
Math Subject Classification: 34B15, 34C10.
Key Words: One-dimensional p-Laplacian, two-point boundary-value problem, superlinear, time mapping.

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Idris Addou
USTHB, Institut de Mathematiques
El-Alia, B.P. no. 32 Bab-Ezzouar
16111, Alger, Algerie.
e-mail: idrisaddou@hotmail.com
Abdelhamid Benmezai
USTHB, Institut de Mathematiques
El-Alia, B.P. no. 32 Bab-Ezzouar
16111, Alger, Algerie.

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