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Existence and Liouville-type theorems for some indefinite quasilinear elliptic problems with potentials vanishing at infinity. (English) Zbl 1181.35101
Summary: We study the existence versus absence of nontrivial weak solutions for a class of indefinite quasilinear elliptic problems on unbounded domains with noncompact boundary in the presence of competing lower order nonlinearities with potentials decaying to zero at infinity.

MSC:
 35J62 Quasilinear elliptic equations 35D30 Weak solutions to PDEs 35B53 Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs
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References:
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