Electron.n. J. Diff. Eqns., Vol. 1999(1999), No. 21, pp. 1-27.

Multiplicity of solutions for quasilinear elliptic boundary-value problems

Idris Addou

This paper is concerned with the existence of multiple solutions to the boundary-value problem
$$-(\varphi_p(u') ) '=\lambda \varphi_q(u) +f(u)\quad\hbox{in }
  (0,1)\,,\quad u(0) =u(1) =0\,,$$
where $p,q$ greater than 1, $\varphi_x(y) =|y|^{x-2}y$, $\lambda $ is a real parameter, and $f$ is a function which may be sublinear, superlinear, or asymmetric. We use the time map method for showing the existence of solutions.

Submitted January 21, 1999. Published June 16, 1999.
Math Subject Classification: 34B15.
Key Words: Multiple solutions, elliptic boundary-value problems.

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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

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