Advances in Differential Equations

Nonexistence results for differential inequalities involving $A$-Laplacian

Agnieszka Kałamajska, Katarzyna Pietruska-Pałuba, and Iwona Skrzypczak

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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 $\Phi$.

Article information

Source
Adv. Differential Equations Volume 17, Number 3/4 (2012), 307-336.

Dates
First available in Project Euclid: 17 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355703088

Mathematical Reviews number (MathSciNet)
MR2919104

Zentralblatt MATH identifier
1260.26019

Subjects
Primary: 26D10: Inequalities involving derivatives and differential and integral operators 35D30: Weak solutions 35J60: Nonlinear elliptic equations 35R45: Partial differential inequalities

Citation

Kałamajska, Agnieszka; Pietruska-Pałuba, Katarzyna; Skrzypczak, Iwona. Nonexistence results for differential inequalities involving $A$-Laplacian. Adv. Differential Equations 17 (2012), no. 3/4, 307--336. https://projecteuclid.org/euclid.ade/1355703088.


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