Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4623931 | Journal of Mathematical Analysis and Applications | 2006 | 16 Pages |
Abstract
This paper is concerned with the existence of solutions for the boundary value problem{â(|uâ²|pâ2uâ²)â²+É|u|pâ2u=âF(t,u),in (0,T),((|uâ²|pâ2uâ²)(0),â(|uâ²|pâ2uâ²)(T))ââj(u(0),u(T)), where É⩾0, pâ(1,â) are fixed, j:RNÃRNâ(ââ,+â] is a proper, convex and lower semicontinuous function and F:(0,T)ÃRNâR is a Carathéodory mapping, continuously differentiable with respect to the second variable and satisfies some usual growth conditions. Our approach is a variational one and relies on Szulkin's critical point theory [A. Szulkin, Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems, Ann. Inst. H. Poincaré Anal. Non Linéaire 3 (1986) 77-109]. We obtain the existence of solutions in a coercive case as well as the existence of nontrivial solutions when the corresponding Euler-Lagrange functional has a “mountain pass” geometry.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Petru Jebelean, Gheorghe MoroÅanu,