American Institute of Mathematical Sciences

March  2008, 7(2): 267-275. doi: 10.3934/cpaa.2008.7.267

Infinitely many solutions for ordinary $p$-Laplacian systems with nonlinear boundary conditions

 1 West University of Timişoara, Department of Mathematics, Blvd. V. Pârvan no. 4, 300223 Timişoara, Romania

Received  July 2006 Revised  April 2007 Published  December 2007

This paper deals with the existence of infinitely many solutions for the boundary value problem

$-( | u' | ^{p-2}u')' + \varepsilon |u|^{p-2}u= \nabla F(t,u),$ in $(0,T)$,

$((|u'|^{p-2}u')(0),$ $-(|u'|^{p-2}u')(T))$ $\in \partial j(u(0), u(T)),$

where $\varepsilon \geq 0$, $p \in (1, \infty)$ are fixed, the convex function $j:\mathbb R^N \times \mathbb R^N \to (- \infty , +\infty ]$ is proper, even, lower semicontinuous and $F:(0,T) \times \mathbb R^N \to \mathbb R$ is a Carathéodory mapping, continuously differentiable and even with respect to the second variable.

Citation: Petru Jebelean. Infinitely many solutions for ordinary $p$-Laplacian systems with nonlinear boundary conditions. Communications on Pure & Applied Analysis, 2008, 7 (2) : 267-275. doi: 10.3934/cpaa.2008.7.267
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