Topological degree methods for partial differential operators in generalized Sobolev spaces

Mustapha Ait Hammou; Elhoussine Azroul; Badr Lahmi

doi:10.5269/bspm.39179

Mustapha Ait Hammou University Sidi Mohamed Ben Abdellah https://orcid.org/0000-0002-3930-3469
Elhoussine Azroul University Sidi Mohamed Ben Abdellah https://orcid.org/0000-0002-2396-4844
Badr Lahmi University Sidi Mohamed Ben Abdellah

Resumo

The main aim of this paper is to prove, by using the topological degree methods, the existence of solutions for nonlinear elliptic equation Au = f where Au is partial dierential operators of general divergence form.

Downloads

Não há dados estatísticos.

Referências

J. Berkovits, On the degree theory for nonlinear mappings of monotone type, Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 58 (1986).

J. Berkovits and V. Mustonen, On topological degree for mappings of monotone type, Nonlinear Anal. 10 (1986), 1373-1383.

J. Berkovits and V. Mustonen, Nonlinear mappings of monotone type I. Classification and degree theory, Preprint No 2/88, Mathematics, University of Oulu.

L. E. J. Brouwer, Uber Abbildung von Mannigfaltigkeiten, Math. Ann. 71 (1912) , 97-115.

FE. Browder, Fixed point theory and nonlinear problems, Bull. Am. Math. Soc. 9(1983), 1-39.

FE. Browder, Degree of mapping for nonlinear mappings of monotone type, Proc. Natl. Acad. Sci. USA 80 (1983), 1771-1773.

K.Deimling, Nonlinar functional analysis, Springer, Berlin (1985).

X. L. Fan and D. Zhao, On the Spaces Lp(x)( ) and Wm,p(x)( ), J. Math. Anal. Appl., 263 (2001), 424-446.

E. Hewitt and K. Strombergs, Real and abstract analysis, Springer-Verlag, Berlin Heidelberg New York, (1965).

S. Hu and N. S. Papageorgiou, Generalizations of Browder’s Degree Theory, Transactions of the American Mathematical Society, 347 (1995), no 1.

O. Kovacik and J. Rakosnık, On spaces Lp(x) and W1,p(x), Czechoslovak Math. J. 41 (1991), 592-618.

J. Leray and J. Schauder, Topologie et equationes fonctionnelles, Ann. Sci. Ec. Norm. Super. 51 (1934), 45-78.

R. Landes 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.

M. Ruzicka, Electrorheological fuids: modeling and mathematical theory, Lecture Notes in Mathematics, 1748, Springer-Verlag, Berlin, (2000) MR 1810360.

IV. Skrypnik, Nonlinear higher order elliptic equations, Naukova Dumka, Kiev (1973)(in Russian).

IV. Skrypnik, Methods for analysis of nonlinear elliptic bondary value problems, Amer. Math. Soc. Transl., Ser. II, vol. 139. AMS, Providence(1994).

M. Tienari, A degree theory for a class of mappings of monotone type in Orlicz-Sobolev spaces, Annales Academiae Scientiarum Fennicae: Mathematica, Suomalainen Tiedeakatemia Helsinki, Vol 97 (1994).

K. Yozida, Functional analysis, Springer-Verlag, Berlin Heidelberg New York (1974).

E. Zeidler, Nonlinear functional analysis and its applications I: Fixed-Point-Theorems, Springer, New York (1985).