Large versus bounded solutions to sublinear elliptic problems

Ewa Damek, Zeineb Ghardallou
2019 Bulletin of the Polish Academy of Sciences Mathematics  
Let L be a second order elliptic operator with smooth coefficients defined on a domain Ω ⊂ R d (possibly unbounded), d ≥ 3. We study nonnegative continuous solutions u to the equation Lu(x) − ϕ(x, u(x)) = 0 on Ω, where ϕ 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. 2010 Mathematics Subject Classification:
more » ... rimary 31D05, 35J08, 35J61; Secondary 31C05. . ( 1 ) By a domain we always mean a set that is open and connected.
doi:10.4064/ba8180-12-2018 fatcat:6crz3edsnvgxvjaq5sijms52wy