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Large versus bounded solutions to sublinear elliptic problems
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:
doi:10.4064/ba8180-12-2018
fatcat:6crz3edsnvgxvjaq5sijms52wy