Electron. J. Diff. Eqns., Vol. 2009(2009), No. 103, pp. 1-13.

Existence and multiplicity results for Singular phi-Laplacian BVPs on the positive half-line

Smail Djebali, Karima Mebarki

This work proves the existence and multiplicity of positive solutions for a second-order nonlinear three-point phi-Laplacian boundary-value problem posed on the positive half-line. The nonlinearity depends on the solution and its derivative and may exhibit a time singularity at the origin. Existence of single and multiple nontrivial positive solutions is proved using fixed point index theory.

Submitted May 14, 2009. Published August 27, 2009.
Math Subject Classifications: 34B10, 34B15, 34B16, 34B18, 34B40.
Key Words: phi-Laplacian; three point BVPs; positive solutions; singularity; fixed point in a cone.

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Smail Djebali
Department of Mathematics, E.N.S.
P.O. Box 92, 16050 Kouba, Algiers, Algeria
email: djebali@ens-kouba.dz, djebali@hotmail.com
Karima Mebarki
Faculty of Fundamental Sciences
U.M.B.B., 35000. Boumerdes, Algeria
email: mebarqi@hotmail.fr

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