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Positive solutions for singularly perturbed nonlinear elliptic problem on manifolds via Morse theory
singular perturbation nondegenerate critical points Morse theory
2011/2/28
Given (M, g0) we consider the problem −"2g0+hu + u = (u+)p−1 with (", h) ∈ (0, ¯") × B. Here B is a ball centered at 0 with radius in the Banach space of all Ck symmetric covaria...
Gradient estimates for a simple nonlinear heat equation on manifolds
nonlinear heat equation gradient estimate
2010/11/29
In this paper, we study the gradient estimate for positive solutions to the following nonlinear heat equation problem ut − u = au log u + V u, u > 0 on the compact Riemannian manifold (M, g) of...