On the nonexistence of positive solutions to doubly nonlinear equations for baouendi-grushin operators
Discrete and Continuous Dynamical Systems- Series A, vol.33, no.11-12, pp.5167-5176, 2013 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 33 Issue: 11-12
- Publication Date: 2013
- Doi Number: 10.3934/dcds.2013.33.5167
- Journal Name: Discrete and Continuous Dynamical Systems- Series A
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.5167-5176
- Keywords: Baouendi-Grushin vector fields, nonlinear parabolic equations, positive solutions, Hardy inequality
- İstanbul Ticaret University Affiliated: Yes
Abstract
The purpose of this paper is to study the nonexistence of positive solutions of the doubly nonlinear equation -u t = r (um-1jrujp-2ru) + V um+p-2 in (0; T); u(x; 0) = u0(x) 0 in ; u(x; t) = 0 on (0; T); where r = (rx; jxj2ry), x 2 Rd; y 2 Rk, > 0, is a metric ball in RN, V 2 L1 loc(), m 2 R, 1 < p < d + k and m + p - 2 > 0. The exponents q are found and the nonexistence results are proved for q m + p < 3.