Document Type
Article
Publication Date
2001
Digital Object Identifier (DOI)
https://doi.org/10.1155/S1085337501000549
Abstract
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| p−2uxi)=−|u| q−1u,Σi=1n(a (x)| uxi | p−2uxi)xi=−|u| q−1u,Σi=1n(a (x)|∇u| p−2uxi/1+|∇u| 2)xi=−|u| q−1u, where n≥1, 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.
Rights Information
This work is licensed under a Creative Commons Attribution 3.0 License.
Was this content written or created while at USF?
Yes
Citation / Publisher Attribution
Abstract and Applied Analysis, v. 6, art. 245068
Scholar Commons Citation
Kartsatos, A. G. and Kurta, V. V., "Nonexistence Theorems for Weak Dolutions of Quasilinear Elliptic Equations" (2001). Mathematics and Statistics Faculty Publications. 81.
https://digitalcommons.usf.edu/mth_facpub/81
