Existence of positive solutions for nonlinear elliptic equations with convection terms. (March 2017) - Motreanu, D.; Tanaka, M.
Abstract: We prove the existence of positive solutions for the equation − ∑ i = 1 N ∂ ∂ x i a i ( x, u, ∇ u ) = f ( x, u, ∇ u ) in Ω under the Dirichlet boundary condition, where the essential point is the dependence of the terms of the elliptic equation on the solution u and its gradient ∇ u . We develop an approach based on approximate solutions and on a new strong maximum principle.