On the nonexistence of positive solutions to doubly nonlinear equations for baouendi-grushin operators

KÖMBE İ.

Discrete and Continuous Dynamical Systems- Series A, cilt.33, sa.11-12, ss.5167-5176, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 33 Sayı: 11-12
  • Basım Tarihi: 2013
  • Doi Numarası: 10.3934/dcds.2013.33.5167
  • Dergi Adı: Discrete and Continuous Dynamical Systems- Series A
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.5167-5176
  • Anahtar Kelimeler: Baouendi-Grushin vector fields, nonlinear parabolic equations, positive solutions, Hardy inequality
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

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.