A strong comparison principle for the -Laplacian期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A strong comparison principle for the -Laplacian

Authors:	Paolo Roselli Berardino Sciunzi

Affiliation:	Dipartimento di Matematica, Universà di Roma ``Tor Vergata', Via della Ricerca Scientifica 00133 Roma, Italy ; Dipartimento di Matematica, Università di Roma ``Tor Vergata', Via della Ricerca Scientifica, 00133 Roma, Italy

Abstract:	We consider weak solutions of the differential inequality of p-Laplacian type such that on a smooth bounded domain in $mathbb{R}^N$ and either or is a weak solution of the corresponding Dirichlet problem with zero boundary condition. Assuming that on the boundary of the domain we prove that , and assuming that on the boundary of the domain we prove unless . The novelty is that the nonlinearity is allowed to change sign. In particular, the result holds for the model nonlinearity $f(s) = s^q - lambda s^{p-1}$ with .

Keywords:	$p$-Laplace operator geometric and qualitative properties of the solutions comparison principle.

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载全文