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Large versus bounded solutions to sublinear elliptic problems

Damek Ewa, Ghardallou Zeineb

Bulletin of the Polish Academy of Sciences. Mathematics

2019

Vol. 67, no. 1

69--82

Let L be a second order elliptic operator with smooth coefficients defined on a domain Ω ⸦ Rd (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.