Existence of positive solutions of singular $p$-Laplacian equations in a ball

Li, Fang¹ ; Yang, Zuodong²

¹ Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Jiangsu Nanjing 210046, China
² College of Zhongbei, Nanjing Normal University, Jiangsu Nanjing 210046, China;Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Jiangsu Nanjing 210046, China

Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 1, p. 44-55.

Résumé

In this paper, we investigate singular $p$-Laplacian equations of the form $\Delta _pu + f(x,\nabla u)u^{-\lambda} = 0$ with zero Dirichlet boundary condition in a ball $B \subset R^N$; where $p > 1, \lambda > 0$, and give a sufficient condition for the equation to have a positive solution, by means of a supersolution and a subsolution.

Détail

DOI : 10.22436/jnsa.005.01.06

Classification : 58J10, 35N20
Keywords: Positive solution, singular equation, supersolution and subsolution.

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