Electron. J. Diff. Eqns., Vol. 2004(2004), No. 69, pp. 1-13.

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

George L. Karakostas

Abstract:
The existence of triple positive solutions for a boundary-value problem governed by the $\Phi$-Laplacian is investigated, when $\Phi$ is a so-called sup-multiplicative-like function (in a sense introduced in [22]) and the boundary conditions include nonlinear expressions at the end points (as in [21, 28]). The Leggett-Williams fixed point theorem in a cone is used. The results improve and generalize known results given in [21].

Submitted February 5, 2004. Published May 6, 2004.
Math Subject Classifications: 34B15, 34B18.
Key Words: Boundary value problems, positive solutions, $\Phi$-Laplacian, Leggett-Williams 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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