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Keywords:
pseudomonotone; mappings of monotone type; Orlicz-Sobolev space; almost solvability; quasi-monotone map; quasimonotone
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.
References:
[1] Adams R.: Sobolev spaces. Academic Press, New York, 1975. MR 0450957 | Zbl 0314.46030
[2] Berkovits J., Mustonen V.: On topological degree for mappings of monotone type. Nonlinear Anal. TMA 10 (1986), 1373-1383. MR 0869546
[3] Browder F. E.: Fixed point theory and nonlinear problems. Bull. Amer. Math. Soc. 9 (1983), 1-39. DOI 10.1090/S0273-0979-1983-15153-4 | MR 0699315 | Zbl 0533.47053
[4] Donaldson, T: Nonlinear elliplic boundary value problems in Orlicz-Sobolev spaces. J. Differential Equations 10 (1971), 507-528. DOI 10.1016/0022-0396(71)90009-X | MR 0298472
[5] Donaldson T., Trudinger N. S.: Orlicz-Sobolev spaces and imbedding theorems. J. Functional Analysis 8 (1971), 52-75. DOI 10.1016/0022-1236(71)90018-8 | MR 0301500 | Zbl 0216.15702
[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. DOI 10.1090/S0002-9947-1974-0342854-2 | MR 0342854
[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
[8] Gossez J.-P.: Some approximation properties in Orlicz-Sobolev spaces. Studia Math. 74 (1982), 17-24. MR 0675429 | Zbl 0503.46018
[9] Gossez J.-P., Mustonen V.: Variational inequalities in Orlicz-Sobolev spaces. Nonlinear Anal. 11 (1987), 379-392. DOI 10.1016/0362-546X(87)90053-8 | MR 0881725 | Zbl 0643.49006
[10] Hess P.: On nonlinear mappings of monotone type with respect to two Banach spaces. J. Math. Pures Appl. 52 (1973), 13-26. MR 0636418 | Zbl 0222.47019
[11] Hewitt E., Stromberg K.: Real and abstract analysis. Springer-Verlag, Berlin, 1965. MR 0367121 | Zbl 0137.03202
[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
[13] Krasnoseľskii M., Rutickii J.: Convex functions and Orlicz spaces. P. Noordhoff Ltd., Groningen, 1961. MR 0126722
[14] Kufner A., John O., Fučík S.: Function spaces. Academia, Praha, 1977. MR 0482102
[15] Landes R.: On Galerkin's method in the existence theory of quasilinear elliptic equations. J. Funct. Anai. 39 (1983), 123-148. DOI 10.1016/0022-1236(80)90009-9 | MR 0597807
[16] Landes R., Mustonen V.: On pseudomonotone operators and nonlinear noncoercive variational problems on unbounded domains. Math. Ann. 248 (1980), 241-246. DOI 10.1007/BF01420527 | MR 0575940
[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. DOI 10.1016/0022-247X(82)90173-1 | MR 0661399
[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
[19] Skrypnik I.: Nonlinear higher order elliptic equations. Naukova Dumka, Kiev, 1973. MR 0435590 | Zbl 0276.35043
[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). MR 2714883 | Zbl 0821.47044
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