Nonexistence of   solutions for nonlineardifferential inequalities with  gradient nonlinearities

Xiaohong Li; Fengquan Li

doi:10.3934/cpaa.2012.11.935

Article Contents

2012, Volume 11, Issue 3: 935-943. Doi: 10.3934/cpaa.2012.11.935

This issue Previous Article Existence of traveling waves with transition layers for some degenerate cross-diffusion systems Next Article Multiple solutions of second-order ordinary differential equation via Morse theory

Nonexistence of solutions for nonlinear differential inequalities with gradient nonlinearities

Xiaohong Li^1, and
Fengquan Li^1,

1.
School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024

Received: July 31, 2010

Revised: September 30, 2011

Published: April 2012

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Abstract

The aim of this paper is to prove some nonexistence results for nonnegative weak solutions of the nonlinear differential inequalities with gradient nonlinearities in $R^N$. The proofs are based on the test function method developed by Bidaut-Véron, Mitidieri and Pohozaev in [3] and [14].

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Mathematics Subject Classification: Primary: 35J60, 35J70; Secondary: 35R45.

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