Large versus bounded solutions to sublinear elliptic problems
Volume 67 / 2019
Bulletin Polish Acad. Sci. Math. 67 (2019), 69-82
MSC: Primary 31D05, 35J08, 35J61; Secondary 31C05.
DOI: 10.4064/ba8180-12-2018
Published online: 15 March 2019
Abstract
Let $L $ be a second order elliptic operator with smooth coefficients defined on a domain $\varOmega \subset \mathbb {R}^d$ (possibly unbounded), $d\geq 3$. We study nonnegative continuous solutions $u$ to the equation $L u(x) - \varphi (x, u(x))=0$ on $\varOmega $, where $\varphi $ is in the Kato class with respect to the first variable and it grows sublinearly with respect to the second variable. Under fairly general assumptions we prove that if there is a bounded nonzero solution then there is no large solution.
