Positive solutions of some elliptic differential equations with oscillating nonlinearity

Details Positive solutions of some elliptic differential equations with oscillating nonlinearity Positive solutions of some elliptic differential equations with oscillating nonlinearity

2010-01-06

arxiv.org/abs/1001.0933v1

Mathematics

Analysis of PDEs

Scientific paper

We discuss the occurrence of positive solutions which decay to 0 as $| x|\to+\infty$ to the differential equation $\Delta u+f(x,u)+g(| x|)x\cdot\nabla u=0$, $| x|>R>0$, $x\in\mathbb{R}^{n}$, where $n\geq 3$, $g$ is nonnegative valued and $f$ has alternating sign, by means of the comparison method. Our results complement several recent contributions from [M. Ehrnstr\"{o}m, O.G. Mustafa, On positive solutions of a class of nonlinear elliptic equations, Nonlinear Anal. TMA 67 (2007), 1147--1154].

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