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INVARIANCE OF DOMAIN THEOREMS FOR CONDENSING MULTIVALUED VECTOR FIELDS

김인숙
대한수학회 (The Korean Mathematical Society)|2010.01|대한수학회보 (Bulletin of the KMS)|제47권 제1호|pp. 121-129

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참고문헌

키워드

degree theoryinvariance of domaincountably condensingmultivalued vector fields
주제분류수학

초록

Using a degree theory for countably condensing multivalued maps, we show that under certain conditions an invariance of domain theorem holds for countably condensing or countably k-contractive multivalued vector fields.

Abstract

Using a degree theory for countably condensing multivalued maps, we show that under certain conditions an invariance of domain theorem holds for countably condensing or countably k-contractive multivalued vector fields.

참고문헌 (14)

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  6. I.-S. Kim, "The invariance of domain theorem for condensing vector fields", Topol. Methods Nonlinear Anal., 25(2), pp.363~373 (2005)
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  9. W. V. Petryshyn, "A degree theory, fixed point theorems, and mapping theorems for multivalued noncompact mappings", Trans. Amer. Math. Soc., 194, pp.1~25 (1974)
  10. J. Schauder, "Invarianz des Gebietes in Funktionalräumen", Studia Math., 1, pp.123~139 (1929)
  11. J. Schauder, "Über den Zusammenhang zwischen der Eindeutigkeit und Lösbarkeit partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus", Math. Ann., 106(1), pp.661~721 (1932)
  12. M. Väth, "Fixed point theorems and fixed point index for countably condensing maps", Topol. Methods Nonlinear Anal., 13(2), pp.341~363 (1999)
  13. M. Väth, "An axiomatic approach to a coincidence index for noncompact function pairs", Topol. Methods Nonlinear Anal., 16(2), pp.307~338 (2000)
  14. M. Väth, "On the connection of degree theory and 0-epi maps", J. Math. Anal. Appl., 2574(1), pp.223~237 (2001)

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