Generalized scalar curvature type equation on complete Riemannian manifolds
Texas State University-San Marcos, Department of Mathematics
In this work, we investigate positive solutions for a quasilinear elliptic equation on complete manifold M. This equation extends to the p-Laplacian the equation of the prescribed scalar curvature. A minimizing sequence is constructed which converges to a non trivial solution belonging to C1,ɑ(K) for any compact set K ⊂ M and some α ∈ (0, 1).
Complete manifolds, p-Laplacian, Critical Sobolev exponent
Benalili, M., & Maliki, Y. (2004). Generalized scalar curvature type equation on complete Riemannian manifolds. <i>Electronic Journal of Differential Equations, 2004</i>(147), pp. 1-18.