| EXISTENCE AND UNIQUENESS OF POSITIVE EIGENVALUES FOR CERTAIN EIGENVALUE SYSTEMS |
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| 作者姓名： | XUE Ruying QIN Yuchun |
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| 作者单位： | Department of Mathematics，Hangzhou University，Hangzhou 310028，China |
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| 摘 要： | 1.IntroductionLetnbeaboundeddomaininR"withsmoothboundaryoa,A.denotethep-Laplaciandefinedbya.~div(IVuIP--'Vu),forpE(1,co),andop.(u)=]nip--'if.ItiswellknownthattheeigenvalueproblemhasauniquepositiveeigenvalueAcforwhichtheeigenvalueproblerll(1.1)possessespositiveeigenfunctions.Infact,andtheeigenfunctionsforAcaretheminimizersofthefunctionalMoreover,suchaminimizerofo6Wt3'(n)existsandisuniqlle11ptoascalarmultiple,andofo6Lab(~);wenormalizeitbyjaba(x)lgholpdx~1andofo2:0inD.Thenalsoofo>0inDandcp…
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EXISTENCE AND UNIQUENESS OF POSITIVE EIGENVALUES FOR CERTAIN EIGENVALUE SYSTEMS |
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| XUE Ruying, QIN Yuchun.EXISTENCE AND UNIQUENESS OF POSITIVE EIGENVALUES FOR CERTAIN EIGENVALUE SYSTEMS[J].Journal of Systems Science and Complexity,1999(2). |
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| Authors: | XUE Ruying QIN Yuchun |
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| Abstract: | In this paper we consider certain eigenvalue systems. Imposing some reasonable hypotheses, we prove that the eigenvalue system has a unique eigenvalue with positive eigenfunctions, and that the eigenfunction is unique up to a scalar multiple. |
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| Keywords: | Eigenvalue problem eigenfunction fixed point index maximum principle |
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