Electron. J. Diff. Eqns., Vol. 2004(2004), No. 68, pp. 1-12.

Positive solutions for the $\Phi$-Laplacian when $\Phi$ is a sup - multiplicative - like function

George L. Karakostas

We provide sufficient conditions for the existence of positive solutions of a boundary-value problem for a one dimensional $\Phi$-Laplacian ordinary differential equation with deviating arguments, where $\Phi$ is a sup-multiplicative-like function (in a sense introduced here) and the boundary conditions include nonlinear expressions at the end points. For this end, we use the Krasnoselskii fixed point theorem in a cone. The results obtained improve and generalize known results in [17] and elsewhere.

Submitted February 5, 2004. Published May 4, 2004.
Math Subject Classifications: 34B15, 34B18.
Key Words: Boundary value problems, positive solutions, Krasnoselskii's fixed point theorem.

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George L. Karakostas
Department of Mathematics
University of Ioannina,
451 10 Ioannina, Greece
email: gkarako@cc.uoi.gr

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