ON SOLVABILITY OF A CLASS OF NONLINEAR ELLIPTIC TYPE EQUATION WITH VARIABLE EXPONENT

SERT U., SOLTANOV K.

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, cilt.7, sa.3, ss.1139-1160, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 7 Sayı: 3
  • Basım Tarihi: 2017
  • Doi Numarası: 10.11948/2017071
  • Dergi Adı: JOURNAL OF APPLIED ANALYSIS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1139-1160
  • Anahtar Kelimeler: PDEs with nonstandart nonlinearity, solvability theorem, variable exponent, implicit degenerate PDEs, LOCALIZATION PROPERTIES, GROWTH-CONDITIONS, REGULARITY, FUNCTIONALS, UNIQUENESS, EXISTENCE
  • Hacettepe Üniversitesi Adresli: Evet

Özet

In this paper, we study the Dirichlet problem for the implicit degenerate nonlinear elliptic equation with variable exponent in a bounded domain Omega subset of R-n. We obtain sufficient conditions for the existence of a solution without regularization and any restriction between the exponents. Furthermore, we define the domain of the operator generated by posed problem and investigate its some properties and also its relations with known spaces that enable us to prove existence theorem.