March/April 2012 Nonexistence results for differential inequalities involving $A$-Laplacian
Agnieszka Kałamajska, Katarzyna Pietruska-Pałuba, Iwona Skrzypczak
Adv. Differential Equations 17(3/4): 307-336 (March/April 2012). DOI: 10.57262/ade/1355703088

Abstract

We give a sufficient condition for nonexistence of nontrivial nonnegative solutions to the partial differential inequality involving $A$-Laplacian: $-\Delta_A u\ge \Phi (u)$, where $u$ is defined on ${{\mathbb{R}^{n}}}$. The condition obtained relies on the rate of decay at infinity of certain functions involving $A$ and $\Phi$. The techniques, based on methods due to Mitidieri and Pohozaev, exploit suitable a priori estimates in the framework of Orlicz-Sobolev spaces. The result is illustrated by logarithmic $A$-Laplacians and logarithmic functions $\Phi$.

Citation

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Agnieszka Kałamajska. Katarzyna Pietruska-Pałuba. Iwona Skrzypczak. "Nonexistence results for differential inequalities involving $A$-Laplacian." Adv. Differential Equations 17 (3/4) 307 - 336, March/April 2012. https://doi.org/10.57262/ade/1355703088

Information

Published: March/April 2012
First available in Project Euclid: 17 December 2012

zbMATH: 1260.26019
MathSciNet: MR2919104
Digital Object Identifier: 10.57262/ade/1355703088

Subjects:
Primary: 26D10 , 35D30 , 35J60 , 35R45

Rights: Copyright © 2012 Khayyam Publishing, Inc.

Vol.17 • No. 3/4 • March/April 2012
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