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


SERT U., SOLTANOV K.

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, vol.7, no.3, pp.1139-1160, 2017 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 3
  • Publication Date: 2017
  • Doi Number: 10.11948/2017071
  • Journal Name: JOURNAL OF APPLIED ANALYSIS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.1139-1160
  • Keywords: PDEs with nonstandart nonlinearity, solvability theorem, variable exponent, implicit degenerate PDEs, LOCALIZATION PROPERTIES, GROWTH-CONDITIONS, REGULARITY, FUNCTIONALS, UNIQUENESS, EXISTENCE

Abstract

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.