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Positive Solutions for the p-Laplacian with Dependence on the Gradient
Positive Solutions the p-Laplacian
2010/11/23
We prove a result of existence of positive solutions of the Dirichlet problem for $-\Delta_p u=\mathrm{w}(x)f(u,\nabla u)$ in a bounded domain $\Omega\subset\mathbb{R}^N$, where $\Delta_p$ is the $p$...
Complete classification of the positive solutions of $-Δu + u^q=0$
positive solutions of $-Δu + u^q=0$
2010/12/9
We study the equation −u+uq = 0, q > 1, in a bounded C2 domain RN. A positive solution of the equation is moderate if it is dominated by a harmonic function and -moderate if it is the limit ...