Variational and topological methods for operator equations involving duality mappings on Orlicz-Sobolev spaces

Dinca, George ; Matei, Pavel

Electronic Journal of Differential Equations, Tome 2007 (2007).

Résumé

Summary: Let $$\displaylines{ J_{a}u=\sum_{| \alpha | }(-1)^{| \alpha | }D^{\alpha }g_{\alpha }(x,D^{\alpha }u) \quad\hbox{in }\Omega , \cr D^{\alpha }u=0\hbox{ on }\partial \Omega , | \alpha | \leq m-1, }$$ where $$ \| u\| _{m,A}=\| \sqrt{T[u,u]}\| _{(A)}, $ \| \cdot \| _{(A)}$ being the Luxemburg norm on $E_{A}(\Omega )$. By using the Leray-Schauder topological degree and the mountain pass theorem of Ambrosetti and Rabinowitz, the existence of nontrivial solutions is established. The results of this paper generalize the existence results for Dirichlet problems with p-Laplacian given in [12] and [13].$$

Détail

Classification : 35B38, 35B45, 47J30, 47H11
Keywords: A priori estimate, critical points, Orlicz-Sobolev spaces, Leray-Schauder topological degree, duality mapping, nemytskij operator, mountain pass theorem