Open Access
16 September 2001 Nonexistence theorems for weak solutions of quasilinear elliptic equations
A. G. Kartsatos, V. V. Kurta
Abstr. Appl. Anal. 6(3): 163-189 (16 September 2001). DOI: 10.1155/S1085337501000549


New nonexistence results are obtained for entire bounded (either from above or from below) weak solutions of wide classes of quasilinear elliptic equations and inequalities. It should be stressed that these solutions belong only locally to the corresponding Sobolev spaces. Important examples of the situations considered herein are the following: Σi=1n(a(x)|u|p2uxi)=|u|q1u,Σi=1n(a(x)|uxi|p2uxi)xi=|u|q1u,Σi=1n(a(x)|u|p2uxi/1+|u|2)xi=|u|q1u, where n1,p>1,q>0 are fixed real numbers, and a(x) is a nonnegative measurable locally bounded function. The methods involve the use of capacity theory in connection with special types of test functions and new integral inequalities. Various results, involving mainly classical solutions, are improved and/or extended to the present cases.


Download Citation

A. G. Kartsatos. V. V. Kurta. "Nonexistence theorems for weak solutions of quasilinear elliptic equations." Abstr. Appl. Anal. 6 (3) 163 - 189, 16 September 2001.


Published: 16 September 2001
First available in Project Euclid: 13 April 2003

zbMATH: 1119.35322
MathSciNet: MR1861245
Digital Object Identifier: 10.1155/S1085337501000549

Primary: 35J60 , 35R45

Rights: Copyright © 2001 Hindawi

Vol.6 • No. 3 • 16 September 2001
Back to Top