Electron. J. Diff. Equ.,
Vol. 2011 (2011), No. 32, pp. 129.
Multiple positive solutions for singular multipoint
boundaryvalue problem with general growth on the positive half line
Smail Djebali, Karima Mebarki
Abstract:
This work is devoted to the existence of nontrivial positive
solutions for a class of secondorder nonlinear multipoint
boundaryvalue problems on the positive halfline. The novelty of
this work is that the nonlinearity may exhibit a singularity at
the origin simultaneously with respect to the solution and its
derivative; moreover it satisfies quite general growth conditions
far from the origin, including polynomial growth. New existence
results of single, twin and triple solutions are proved using the
fixed point index theory on appropriate cones in weighted Banach
spaces together with twofunctional and threefunctional fixed
point theorems. The singularity is treated by means of
approximation and compactness arguments. The proofs of the
existence results rely heavily on several sharp estimates and
useful properties of the corresponding Green's function.
Submitted August 26, 2010. Published February 23, 2011.
Math Subject Classifications: 34B15, 34B16, 34B18, 34B40.
Key Words: Fixed point; multiple solutions; multipoint; singularity;
infinite interval; cone.
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Smaïl Djebali
Department of Mathematics, E.K.S.,
PO Box 92, 16050 Kouba. Algiers, Algeria
email: djebali@enskouba.dz, djebali@hotmail.com


Karima Mebarki
Department of Mathematics
A.E. Mira University, 06000. Bejaia, Algeria
email: mebarqi@hotmail.fr

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