On Positive Solutions of Semilinear Elliptic Equations
Open Access
- 1 November 1987
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 101 (3) , 445-452
- https://doi.org/10.2307/2046386
Abstract
This paper is concerned with necessary conditions for the existence of positive solutions of the semilinear problem <!-- MATH $\Delta u + f(u) = 0,x \in \Omega ,u = 0,x \in \partial \Omega$ --> , whose supremum norm bears a certain relationship to zeros of the nonlinearity . We first discuss the smooth case (i.e., and <!-- MATH $\partial \Omega$ --> smooth) and then show how to obtain similar results in the nonsmooth case.
Keywords
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