一类非线性四阶特征值问题的正解

Abstract

CLC Number:

34B15

FEI Xiang-Li, BAI Zhan-Bing. On Positive Solutions of Some Nonlinear Fourth-Order Eigenvalue Problems[J].Acta mathematica scientia,Series A, 2001, 21(zk): 610-615.

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１　ＡｇａｒｗａｌＲＰ．Ｏｎｆｏｕｒｔｈｏｒｄｅｒｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓａｒｉｓｉｎｇｉｎｂｅａｍａｎａｌｙｓｉｓ，ＤｉｆｆｅｒｅｎｔｉａｌＩｎｔｅｇｒａｌＥｑｕａｔｉｏｎｓ．１９８９，２：９１－１１０
２　ＢａｉＺＢ．Ｔｈｅｍｅｔｈｏｄｏｆｌｏｗｅｒａｎｄｕｐｐｅｒｓｏｌｕｔｉｏｎｓｆｏｒａｂｅｎｄｉｎｇｏｆａｎｅｌａｓｔｉｃｂｅａｍｅｑｕａｔｉｏｎ，ＪＭａｔｈＡｎａｌＡｐｐｌ，２０００，２４８：１９５－２０２
３　ＥｒｂｅＬＨ，ＨｕＳ，ＷａｎｇＨＹ．Ｍｕｌｔｉｐｌｅｐｏｓｉｔｉｖｅｓｏｌｕｔｉｏｎｓｏｆｓｏｍｅｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓ，ＪＭａｔｈＡｎａｌＡｐｐｌ，１９９４，１８４：６４０－６４８
４　ＦｉｎｋＡＭ，ＧａｔｉｃａＪＡ，ＨｅｒｎａｎｄｅｚＧＥ．ＥｉｇｅｎｖａｌｕｅｓｏｆｇｅｎｅｒａｌｉｚｅｄＧｅｌ＇ｆａｎｄｍｏｄｅｌｓ．ＮｏｎｌＡｎａｌ，１９９３，２０：１４５３－１４６８
５　ＧｕｏＤ，ＬａｋｓｈｍｉｋａｎｔｈａｍＶ．ＮｏｎｌｉｎｅａｒＰｒｏｂｌｅｍｓｉｎＡｂｓｔｒａｃｔＣｏｎｅｓ．ＮｅｗＹｏｒｋ：ＡｃａｄｅｍｉｃＰｒｅｓｓ，１９８８
６　ＧｕｐｔａＣＰ．Ｅｘｉｓｔｅｎｃｅａｎｄｕｎｉｑｕｅｎｅｓｓｒｅｓｕｌｔｓｆｏｒｓｏｍｅｆｏｕｒｔｈｏｒｄｅｒｆｕｌｌｙｑｕａｓｉｌｉｎｅａｒｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍ．ＡｐｐｌｉｃａｂｌｅＡｎａｌｙｓｉｓ１９９０，３６：１５７－１６９
７　ＧｕｓｔａｆｓｏｎＧＢ，Ｓｃｈｍｉｔｔ．Ｍｅｔｈｏｄｏｆｎｏｎｌｉｎｅａｒａｎａｌｙｓｉｓｉｎｔｈｅｔｈｅｏｒｙｏｆｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ．Ｌｅｃｔｕｒｅｎｏｔｅｓ，ＵｎｉｖｅｒｓｉｔｙｏｆＵｔａｈ，１９７５
８　ＨｅｎｄｅｒｓｏｎＪ，ＷａｎｇＨＹ．Ｐｏｓｉｔｉｖｅｓｏｌｕｔｉｏｎｓｆｏｒｎｏｎｌｉｎｅａｒｅｉｇｅｎｖａｌｕｅｐｒｏｂｌｅｍｓ．ＪＭａｔｈＡｎａｌＡｐｐｌ，１９９７，２０８：２５２－２５９
９　ＫｒａｓｎｏｓｅｌｓｋｉｉＭＡ．Ｐｏｓｉｔｉｖｅｓｏｌｕｔｉｏｎｓｏｆｏｐｅｒａｔｏｒｅｑｕａｔｉｏｎｓ．Ｎｏｏｒｄｈｏｆｆ，Ｇｒｏｎｉｎｇｅｎ，１９６４
１０　ＬｉａｎＷＣ，ＷｏｎｇＦＨ，ＹｅｈＣＣ．Ｏｎｔｈｅｅｘｉｓｔｅｎｃｅｏｆｐｏｓｉｔｉｖｅｓｏｌｕｔｉｏｎｓｏｆｎｏｎｌｉｎｅａｒｓｅｃｏｎｄｏｒｄｅｒｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ．ＰｒｏｃＡｍｅｒＭａｔｈＳｏｃ，１９９６，１２４：１１１７－１１２６
１１　ＬｉｕＺＬ，ＬｉＦＹ．Ｍｕｌｔｉｐｌｅｐｏｓｉｔｉｖｅｓｏｌｕｔｉｏｎｓｏｆｎｏｎｌｉｎｅａｒｔｗｏｐｏｉｎｔｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍ．ＪＭａｔｈＡｎａｌＡｐｐｌ，１９９６，２０３：６１０－６２５
１２　ＭａＲＹ，ＷａｎｇＨＹ．Ｏｎｔｈｅｅｘｉｓｔｅｎｃｅｏｆｐｏｓｉｔｉｖｅｓｏｌｕｔｉｏｎｓｏｆｆｏｕｒｔｈｏｒｄｅｒｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ．ＡｐｐｌｉｃａｂｌｅＡｎａｌｙｓｉｓ，１９９５，５９：２２５－２３１
１３　ＭａＲＹ，ＺｈａｎｇＪＨ，ＦｕＳＭ．Ｔｈｅｍｅｔｈｏｄｏｆｌｏｗｅｒａｎｄｕｐｐｅｒｓｏｌｕｔｉｏｎｓｆｏｒｆｏｕｒｔｈｏｒｄｅｒｔｗｏｐｏｉｎｔｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓ．ＪＭａｔｈＡｎａｌＡｐｐｌ，１９９７，２１５：４１５－４２２
１４　姚庆六，白占兵．狌（４）（狋）λ犺（狋）犳（狌（狋））＝０的边值问题的正解存在性．数学年刊，１９９９，２０犃（５）：５７５－５７８

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On Positive Solutions of Some Nonlinear Fourth-Order Eigenvalue Problems

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