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Solving \(p\)-Laplacian equations on complete manifolds. (English) Zbl 1113.58014
Summary: 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 \(k,K: M\to \mathbb{R}\).

MSC:
58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
31C45 Other generalizations (nonlinear potential theory, etc.)
35J60 Nonlinear elliptic equations
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