Monotonicity of the Solutions of Some Quasilinear Elliptic Equations in the Half-plane, and Applications
نویسنده
چکیده
We consider weak positive solutions of the equation −∆mu = f(u) in the halfplane with zero Dirichlet boundary conditions. Assuming that the nonlinearity f is locally Lipschitz continuous and f(s) > 0 for s > 0, we prove that any solution is monotone. Some Liouville type theorems follow in the case of Lane-Emden-Fowler type equations. Assuming also that |∇u| is globally bounded, our result implies that solutions are one-dimensional, and the level sets are flat.
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