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The Liouville theorems for elliptic equations with nonstandard growth. (English) Zbl 1329.35084

Summary: We study solutions and supersolutions of homogeneous and nonhomogeneous \(\mathcal A\)-harmonic equations with nonstandard growth in \(\mathbb{R}^n\). Various Liouville-type theorems and nonexistence results are proved. The discussion is illustrated by a number of examples.

MSC:

35B53 Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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References:

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