Solvability for some boundary value problems with $\phi$-Laplacian operators

J. Ángel Cid; Pedro J. Torres

doi:10.3934/dcds.2009.23.727

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2009, Volume 23, Issue 3: 727-732. Doi: 10.3934/dcds.2009.23.727

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Solvability for some boundary value problems with $\phi$-Laplacian operators

J. Ángel Cid^1, and
Pedro J. Torres^2,

1.
Departamento de Matemáticas, Universidad de Jaén, Campus Las Lagunillas, Jaén
2.
Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada Campus de Fuentenueva s/n, 18071 Granada

Received: September 30, 2007

Revised: May 31, 2008

Published: August 2009

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Abstract

We study the existence of solution for the one-dimensional $\phi$-laplacian equation $(\phi(u'))'=\lambda f(t,u,u')$ with Dirichlet or mixed boundary conditions. Under general conditions, an explicit estimate $\lambda_0$ is given such that the problem possesses a solution for any $|\lambda|<\lambda_0$.

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Mathematics Subject Classification: Primary: 34B15.

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