Asymptotic Behavior of Solutions for Some Nonlinear Partial Differential Equations on Unbounded Domains
Date
2001-12-14
Authors
Fleckinger, Jacqueline
Harrell, Evans M.
de Thelin, Francois
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We study the asymptotic behavior of positive solutions u of
-∆pu(x) = V(x)u(x) p-1, p > 1; x ∈ Ω,
and related partial differential inequalities, as well as conditions for existence of such solutions. Here, Ω contains the exterior of a ball in ℝN 1 < p < N, ∆p is the p-Laplacian and V is a nonnegative function. Our methods include generalized Riccati transformations, comparison theorems, and the uncertainty principle.
Description
Keywords
p-Laplacian, Riccati, Uncertainty principle
Citation
Fleckinger, J., Harrell, E. M., & de Thelin, F. (2001). Asymptotic behavior of solutions for some nonlinear partial differential equations on unbounded domains. <i>Electronic Journal of Differential Equations, 2001</i>(77), pp. 1-14.