Abstract and Applied Analysis
Volume 6 (2001), Issue 3, Pages 163-189
Nonexistence theorems for weak solutions of quasilinear elliptic equations
1Department of Mathematics, University of South Florida, Tampa 33620-5700, FL, USA
2416 Fourth Street, P.O. Box 8604, Ann Arbor, MI 48107-8604, USA
Received 14 April 2001
Copyright © 2001 A. G. Kartsatos and V. V. Kurta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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: ,,, where
are fixed real numbers, and
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.