TY - JOUR T1 - CONSTRUCTION OF A TOPOLOGICAL DEGREE THEORY IN GENERALIZED SOBOLEV SPACES AU - Ait Hammou, Mustapha AU - Azroul, Elhoussine PY - 2018 DA - July Y2 - 2018 JF - Journal of Universal Mathematics JO - JUM PB - Gökhan ÇUVALCIOĞLU WT - DergiPark SN - 2618-5660 SP - 116 EP - 129 VL - 1 IS - 2 LA - en AB - In this paper, we construct an integer-valued degree function in a suitable classes of mappings of monotone type, using a complementary system formed of Generalized Sobolev Spaces in which the variable exponent p in P(log)(Omega) satisfy 1 < p'- < p'+ < + ifinity, where Omega is in RN is open and bounded.This kind of spaces are not refexives KW - Primary Topological degree KW - Generalized Sobolev spaces KW - Secondary Complementary system CR - Berkovits, J.: On the degree theory for nonlinear mappings of monotone type. -Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 58,1986. CR - Berkovits, J., and V. Mustonen: On topological degree for mappings of monotone type. Nonlinear Anal. 10,1986,1373-1383. CR - Berkovits, J., and V. Mustonen: Nonlinear mappings of monotone type I. Classification and degree theory. Preprint No 2/88, Mathematics, University of Oulu. CR - Brouwer, L. E. J: Uber Abbildung von Mannigfaltigkeiten. - Math. Ann. 71, 1912 ,97-115. CR - F. E. Browder, Fixed point theory and nonlinear problems, Bull. Amer. Math. Soc. 9 (1983) 139. CR - Browder, F E: Degree of mapping for nonlinear mappings of monotone type. Proc. Natl. Acad. Sci. USA 80, 1771-1773 (1983). CR - Deimling, K: Nonlinar functional analysis. Springer, Berlin (1985). CR - L. Dingien, P. Harjulehto, P. Hasto, M. Ruzicka: Lebesgue and Sobolev Spaces with Variable Exponents, Springer (2011). CR - L. Fuhrer, Ein elementarer analytischer Beweis zur Eindeutigkeit des A bbildungsgrades im Rn, Math. Nachr. 54 (1972), 259-267. CR - J. P. Gossez; Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients, Trans. Am. Math. Soc. 190 (1974), 163-205. CR - O. Kovacik and J. Rakosnik: On spaces Lp(x) and W1;p(x), Czechoslovak Math. J. 41 (1991), 592-618. CR - Leray, J, Schauder, J: Topologie et equationes fonctionnelles. Ann. Sci. Ec. Norm. Super. 51, 45-78 (1934). CR - Landes, R., and V. Mustonen: Pseudo-monotne mappings in Orlicz-Sobolev spaces and nonlinear boundary value problems on unbounded domains. J. Math. Anal. 88,1982,25-36. CR - Narici, L., and E. Beckenstein: Topological vector spaces. -Marcel Dekker, Inc., New York and Basel, 1985. CR - Skrypnik, I V. : Nonlinear higher order elliptic equations. Naukova Dumka, Kiev (1973)(in Russian). CR - Skrypnik,IV: Methods for analysis of nonlinear elliptic bondary value problems. Amer. Math. Soc. Transl., Ser. II, vol. 139. AMS, Providence(1994). CR - H. Amann and S. Weiss, On the uniqueness of the topological degree, Math. Z. 130 (1973), 39-5. CR - Zeidler, E: Nonlinear functional analysis and its applications I: Fixed-Point-Theorems.Springer, New York (1985). UR - https://dergipark.org.tr/en/pub/jum/issue//423960 L1 - https://dergipark.org.tr/en/download/article-file/519583 ER -