Geodesic
Solving \(p\)-Laplacian equations on complete manifolds
Electronic journal of differential equations, Tome 2006 (2006)
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 $k,K:M\to \mathbb{R}$.
Classification : 31C45, 53C21
Keywords: differential geometry, nonlinear partial differential equations 
@article{EJDE_2006__2006__a53,
     author = {Benalili,  Mohammed and Maliki,  Youssef},
     title = {Solving {\(p\)-Laplacian} equations on complete manifolds},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1113.58014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a53/}
}
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Benalili,  Mohammed; Maliki,  Youssef. Solving \(p\)-Laplacian equations on complete manifolds. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a53/