Ordinary p-Laplacian systems with nonlinear boundary conditions
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- 作者：Petru Jebelean and Gheorghe Moroş ; anu
- 关键词：Ordinary vector p-Laplacian ; Critical point ; Palais– ; Smale condition ; Mountain pass theorem
- 刊名：Journal of Mathematical Analysis and Applications
- 出版年：2006
- 出版时间：15 January 2006
- 年：2006
- 卷：313
- 期：2
- 页码：738-753
- 全文大小：138 K
文摘
This paper is concerned with the existence of solutions for the boundary value problem
where 0, p(1,∞) are fixed, is a proper, convex and lower semicontinuous function and 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.