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초록· 키워드
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Using an index theory for countably condensing maps,
we show the existence of eigenvalues for countably k-set contractive maps and countably condensing maps in an infinite dimensional Banach space X, under certain condition that depends on the quantitative characteristic, that is, the infimum of all k≥ 1 for which there is a countably k-set-contractive retraction of the closed unit ball of X onto its boundary.
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참고문헌 (12)
참고문헌 신청
D. Caponetti / 2005 / Proper 1-ball contractive retractions in Banach spaces of measurable functions / Bull. Austral. Math. Soc. 72 (2) : 299 ~ 315
D. Caponetti / 2006 / An extension of Guo’s theorem via k- -contractive retractions / Nonlinear Anal. 64 (9) : 1897 ~ 1907
D. Guo / 1981 / Eigenvalues and eigenvectors of nonlinear operators / Chin. Ann. Math. 2 : 65 ~ 80
F. E. Browder / 1984 / Remarks on the paper in Boundary conditions for condensing mappings / Nonlinear Anal. 8 (9) : 1113 ~
H. M¨onch / 1980 / Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces / Nonlinear Anal. 4 (5) : 985 ~ 999
D. Caponetti / 2006 / An extension of Guo’s theorem via k- -contractive retractions / Nonlinear Anal. 64 (9) : 1897 ~ 1907
D. Guo / 1981 / Eigenvalues and eigenvectors of nonlinear operators / Chin. Ann. Math. 2 : 65 ~ 80
F. E. Browder / 1984 / Remarks on the paper in Boundary conditions for condensing mappings / Nonlinear Anal. 8 (9) : 1113 ~
H. M¨onch / 1980 / Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces / Nonlinear Anal. 4 (5) : 985 ~ 999
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