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Title: On monotone-like mappings in Orlicz-Sobolev spaces (English)
Author: Mustonen, Vesa
Author: Tienari, Matti
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 124
Issue: 2
Year: 1999
Pages: 255-271
Summary lang: English
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Category: math
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Summary: We study the mappings of monotone type in Orlicz-Sobolev spaces. We introduce a new class $(S_m)$ as a generalization of $(S_+)$ and extend the definition of quasimonotone map. We also prove existence results for equations involving monotone-like mappings. (English)
Keyword: pseudomonotone
Keyword: mappings of monotone type
Keyword: Orlicz-Sobolev space
Keyword: almost solvability
Keyword: quasi-monotone map
Keyword: quasimonotone
MSC: 35J40
MSC: 35J65
MSC: 46E35
MSC: 47H05
MSC: 47H15
MSC: 47H30
MSC: 47J05
idZBL: Zbl 0940.47042
idMR: MR1780696
DOI: 10.21136/MB.1999.126248
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Date available: 2009-09-24T21:37:50Z
Last updated: 2020-07-29
Stable URL: http://hdl.handle.net/10338.dmlcz/126248
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Reference: [1] Adams R.: Sobolev spaces.Academic Press, New York, 1975. Zbl 0314.46030, MR 0450957
Reference: [2] Berkovits J., Mustonen V.: On topological degree for mappings of monotone type.Nonlinear Anal. TMA 10 (1986), 1373-1383. MR 0869546
Reference: [3] Browder F. E.: Fixed point theory and nonlinear problems.Bull. Amer. Math. Soc. 9 (1983), 1-39. Zbl 0533.47053, MR 0699315, 10.1090/S0273-0979-1983-15153-4
Reference: [4] Donaldson, T: Nonlinear elliplic boundary value problems in Orlicz-Sobolev spaces.J. Differential Equations 10 (1971), 507-528. MR 0298472, 10.1016/0022-0396(71)90009-X
Reference: [5] Donaldson T., Trudinger N. S.: Orlicz-Sobolev spaces and imbedding theorems.J. Functional Analysis 8 (1971), 52-75. Zbl 0216.15702, MR 0301500, 10.1016/0022-1236(71)90018-8
Reference: [6] Gossez J.-P.: Nonlinear elliptic boundary value prolems for equations with rapidly (or slowly) increasing coefficients.Trans. Am. Malh. Soc. 190 (1974), 163-205. MR 0342854, 10.1090/S0002-9947-1974-0342854-2
Reference: [7] Gossez J.-P.: Orlicz spaces and nonlinear elliptic boundary value problems.Nonlinear Analysis, Function Spaces and Applications, Teubner-Texte zur Mathematik. 1979, pp. 59-94. MR 0578910
Reference: [8] Gossez J.-P.: Some approximation properties in Orlicz-Sobolev spaces.Studia Math. 74 (1982), 17-24. Zbl 0503.46018, MR 0675429, 10.4064/sm-74-1-17-24
Reference: [9] Gossez J.-P., Mustonen V.: Variational inequalities in Orlicz-Sobolev spaces.Nonlinear Anal. 11 (1987), 379-392. Zbl 0643.49006, MR 0881725, 10.1016/0362-546X(87)90053-8
Reference: [10] Hess P.: On nonlinear mappings of monotone type with respect to two Banach spaces.J. Math. Pures Appl. 52 (1973), 13-26. Zbl 0222.47019, MR 0636418
Reference: [11] Hewitt E., Stromberg K.: Real and abstract analysis.Springer-Verlag, Berlin, 1965. Zbl 0137.03202, MR 0367121
Reference: [12] Kittilä A.: On the topological degree for a ciass of mappings of monotone type and applications to strongly nonlinear elliptic problems.Ann. Acad. Sci. Fenn. Ser. AI Math. Dissertationes 91 (1994). MR 1263099
Reference: [13] Krasnoseľskii M., Rutickii J.: Convex functions and Orlicz spaces.P. Noordhoff Ltd., Groningen, 1961. MR 0126722
Reference: [14] Kufner A., John O., Fučík S.: Function spaces.Academia, Praha, 1977. MR 0482102
Reference: [15] Landes R.: On Galerkin's method in the existence theory of quasilinear elliptic equations.J. Funct. Anai. 39 (1983), 123-148. MR 0597807, 10.1016/0022-1236(80)90009-9
Reference: [16] Landes R., Mustonen V.: On pseudomonotone operators and nonlinear noncoercive variational problems on unbounded domains.Math. Ann. 248 (1980), 241-246. MR 0575940, 10.1007/BF01420527
Reference: [17] Landes R., Mustonen V.: Pseudo-monotone mappings in Orlicz-Sobolev spaces and nonlinear boundary value problem on unbounded domains.J. Math. Anal. Appl. 88 (1982), 25-36. MR 0661399, 10.1016/0022-247X(82)90173-1
Reference: [18] Leray J., Lions J. L.: Quelques résultats de Višik sur des problémes elliptiques non linéaires par les méthodes de Minty-Browder.Bul. Soc. Math. France 93 (1965), 97-107. MR 0194733, 10.24033/bsmf.1617
Reference: [19] Skrypnik I.: Nonlinear higher order elliptic equations.Naukova Dumka, Kiev, 1973. Zbl 0276.35043, MR 0435590
Reference: [20] Tienari M.: A degree theory for a class of mappings of monotone type in Orlicz-Sobolev spaces.Ann. Acad. Sci. Fenn. Ser. AI Math. Dissertationes 97 (1994). Zbl 0821.47044, MR 2714883
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