Existence of a positive solution for quasilinear elliptic equations with nonlinearity including the gradient
Department of Mathematics, Tokyo University of Science, Kagurazaka 1-3, Shinjyuku-ku, Tokyo, 162-8601, Japan
Boundary Value Problems 2013, 2013:173 doi:10.1186/1687-2770-2013-173Published: 24 July 2013
We provide the existence of a positive solution for the quasilinear elliptic equation
in Ω under the Dirichlet boundary condition. As a special case (), our equation coincides with the usual p-Laplace equation. The solution is established as the limit of a sequence of positive solutions of approximate equations. The positivity of our solution follows from the behavior of as t is small. In this paper, we do not impose the sign condition to the nonlinear term f.
MSC: 35J92, 35P30.