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

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

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 $|\lambda|<\lambda_0$.
Citation: J. Ángel Cid, Pedro J. Torres. Solvability for some boundary value problems with $\phi$-Laplacian operators. Discrete & Continuous Dynamical Systems - A, 2009, 23 (3) : 727-732. doi: 10.3934/dcds.2009.23.727
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