Electron. J. Diff. Eqns., Vol. 2006(2006), No. 155, pp. 1-9.

Solving p-Laplacian equations on complete manifolds

Mohammed Benalili, Youssef Maliki

Abstract:
Using a reduced version of the sub and super-solutions method, we prove that the equation $\Delta _{p}u+ku^{p-1}-Ku^{p^{\ast }-1}=0$ has a positive solution on a complete Riemannian manifold for appropriate functions $k,K:M\to \mathbb{R}$.

Submitted June 28, 2005. Published December 14, 2006.
Math Subject Classifications: 31C45, 53C21.
Key Words: Differential geometry; nonlinear partial differential equations.

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Mohammed Benalili
Université Abou - Bekr Belkaïd
Faculté des sciences
Départ. Mthématiques
B.P. 119, Tlemcen, Algerie
email: m_benalili@mail.univ-tlemcen.dz
Youssef Maliki
Université Abou - Bekr Belkaïd
Faculté des sciences
Départ. Mthématiques
B.P. 119, Tlemcen, Algerie
email: malyouc@yahoo.fr

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