Partial Differential Equations
A fixed point method for the p()-Laplacian
Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 757-762.

A topological method, based on the fundamental properties of the Leray–Schauder degree, is used in proving the existence of a week solution in W01,p()(Ω) to Dirichlet problem

div(|u|p(x)2u)=f(x,u),xΩ,(P)
u=0,xΩ.
This method is an adaptation of that used by Dinca et al. [G. Dinca, P. Jebelean, Une méthode de point fixe pour le p-laplacien, C. R. Acad. Sci. Paris, Ser. I 324 (1997) 165–168. [1], G. Dinca, P. Jebelean, J. Mawhin, Variational and topological methods for Dirichlet problems with p-Laplacian, Portugal. Math. 53 (3) (2001) 339–377. [2]] for Dirichlet problems with classical p-Laplacian (p(x)p=const.>1).

On utilise une méthode topologique, basée sur les propriétés fondamentales du degré de Leray–Schauder, afin de démontrer l'existence d'une solution faible dans W01,p()(Ω) pour le problème de Dirichlet (P). Cette méthode représente une adaptation de celle utilisée par Dinca et al. [G. Dinca, P. Jebelean, Une méthode de point fixe pour le p-laplacien, C. R. Acad. Sci. Paris, Ser. I 324 (1997) 165–168. [1], G. Dinca, P. Jebelean, J. Mawhin, Variational and topological methods for Dirichlet problems with p-Laplacian, Portugal. Math. 53 (3) (2001) 339–377. [2]] pour le p-laplacien classique (p(x)p=cte.>1).

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Published online:
DOI: 10.1016/j.crma.2009.04.022
Dinca, George 1

1 Faculty of Mathematics and Computer Science, 14, Academiei St, 010014 Bucharest, Romania
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Dinca, George. A fixed point method for the $ p(\cdot )$-Laplacian. Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 757-762. doi : 10.1016/j.crma.2009.04.022. http://www.numdam.org/articles/10.1016/j.crma.2009.04.022/

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[2] Dinca, G.; Jebelean, P.; Mawhin, J. Variational and topological methods for Dirichlet problems with p-Laplacian, Portugal. Math., Volume 53 (2001) no. 3, pp. 339-377

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