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July  2009, 23(3): 727-732. doi: 10.3934/dcds.2009.23.727

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, Spain
2. 

Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada Campus de Fuentenueva s/n, 18071 Granada, Spain

Received  October 2007 Revised  June 2008 Published  November 2008

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 $|\lambda|<\lambda_0$.
Keywords: mixed boundary value problem, Schauder fixed point theorem, Dirichlet boundary value problem, $\phi$-Laplacian.
Mathematics Subject Classification: Primary: 34B15.
Citation: J. Ángel Cid, Pedro J. Torres. Solvability for some boundary value problems with $\phi$-Laplacian operators. Discrete and Continuous Dynamical Systems, 2009, 23 (3) : 727-732. doi: 10.3934/dcds.2009.23.727
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