Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5024817 | Nonlinear Analysis: Theory, Methods & Applications | 2017 | 23 Pages |
Abstract
We prove the existence of positive solutions for the equation ââi=1Nââxiai(x,u,âu)=f(x,u,âu)inΩ 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 âu. We develop an approach based on approximate solutions and on a new strong maximum principle.
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Authors
D. Motreanu, M. Tanaka,