方程Δu+g(|X|)f(u)=0的环上Dirichlet边值问题的正对径解的存在性

Abstract

Abstract:

We study the existence of positive radial solutions of elliptic equations Δu+\{g(|X|)f(u)\}=0 in annular domains, subject to Dirichlet boundary conditions. In this paper it is no required that liml→0f(l)/l,liml→∞f(l)/l exist. Our worke is a develop to Coffman [7] and Wang Haiyan [9].

Key words: Ｓｅｃｏｎｄｏｒｄｅｒｅｌｌｉｐｔｉｃｅｑｕａｔｉｏｎ, Ｄｉｒｉｃｈｌｅｔｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍ, Ｐｏｓｉｔｉｖｅｒａｄｉａｌｓｏｌｕｔｉｏｎ

CLC Number:

３５Ｊ２０，３４Ｂ１５

Yao Qingliu. Existence of Positive Radial Solutions of Dirichlet Problems for Elliptic Equations Δu+g(|X|)f(u)=0 in Annulus[J].Acta mathematica scientia,Series A, 2000, 20(3): 414-418.

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References

１　ＬｉｏｎｓＰＬ．Ｏｎｔｈｅｅｘｉｓｔｅｎｃｅｏｆｐｏｓｉｔｉｖｅｓｏｌｕｔｉｏｎｓｏｆｓｅｍｉｌｉｎｅａｒｅｌｌｉｐｔｉｃｅｑｕａｔｉｏｎｓ．ＳＩＡＭＲｅｖ，１９８２，２４：４４１－４６７
２　ＮｉＷｅｉｍｉｎｇ．ＵｎｉｑｕｅｎｅｓｓａｎｄｎｏｎｕｎｉｑｕｅｎｅｓｓｆｏｒｐｏｓｉｔｉｖｅｒａｄｉａｌｓｏｌｕｔｉｏｎｓｏｆΔu＋f（u，r）＝０．ＣｏｍｍＰｕｒｅＡｐｐｌＭａｔｈ，
１９８５，３８（１）：６７－１０８
３　ＢａｎｄｌｅＣ，ＣｏｆｆｍａｎＣＶ，ＭａｒｃｕｓＭ．Ｎｏｎｌｉｎｅａｒｅｌｌｉｐｔｉｃｐｒｏｂｌｅｍｓｉｎａｎｎｕｌａｒｄｏｍａｉｎｓ．ＪＤｉｆｆＥｑｎｓ，１９８７，６９：３２２－３４５
４　ＧａｒａｉｚａｒＸ．Ｅｘｉｓｔｅｎｃｅｏｆｐｏｓｉｔｉｖｅｒａｄｉａｌｓｏｌｕｔｉｏｎｓｆｏｒｓｅｍｉｌｉｎｅａｒｅｌｌｉｐｔｉｃｅｑｕａｔｉｏｎｓｉｎｔｈｅａｎｎｕｌｕｓ．ＪＤｉｆｆＥｑｎｓ，１９８７，７０：６９－９２
５　ＬｉｕＳｏｎｇｓｕｎ．Ｏｎｔｈｅｅｘｉｓｔｅｎｃｅｏｆｐｏｓｉｔｉｖｅｒａｄｉａｌｓｏｌｕｔｉｏｎｓｆｏｒｎｏｎｌｉｎｅａｒｅｌｌｉｐｔｉｃｅｑｕａｔｉｏｎｓｉｎａｎｎｕｌａｒｄｏｍａｉｎｓ．ＪＤｉｆｆＥｑｎｓ，１９８９，８１：２２１－２３３
６　ＢａｎｄｌｅＣ，ＫｗａｎｇＭＫ．Ｓｅｍｉｌｉｎｅａｒｅｌｌｉｐｔｉｃｐｒｏｂｌｅｍｓｉｎａｎｎｕｌａｒｄｏｍａｉｎｓ．ＪＡｐｐｌＭａｔｈＰｈｙｓ，１９８９，４０：２４５－２５７
７　ＣｏｆｆｍａｎＣＶ，ＭａｒｃｕｓＭ．ＥｘｉｓｔｅｎｃｅａｎｄｕｎｉｑｕｅｎｅｓｓｒｅｓｕｌｔｓｆｏｒｓｅｍｉｌｉｎｅａｒＤｉｒｉｃｈｌｅｔｐｒｏｂｌｅｍｓｉｎａｎｎｕｌｕｓ．ＡｒｃｈＲａｔｉｏｎａｌＭｅｃｈＡｎａｌ，１９８９，１０８：２９３－３０７
８　ＤａｎｇＨ，ＳｃｈｍｉｔＫ．Ｅｘｉｓｔｅｎｃｅｏｆｐｏｓｉｔｉｖｅｓｏｌｕｔｉｏｎｓｆｏｒｓｅｍｉｌｉｎｅａｒｅｌｌｉｐｔｉｃｅｑｕａｉｔｏｎｓｉｎａｎｎｕｌａｒｄｏｍａｉｎｓ．ＤｉｆｆａｎｄＩｎｔｅｇＥｑｎｓ，１９９４，７：７４７－７５８
９　ＷａｎｇＨａｉｙａｎ．Ｏｎｔｈｅｅｘｉｓｔｅｎｃｅｏｆｐｏｓｉｔｉｖｅｓｏｌｕｔｉｏｎｓｆｏｒｓｅｍｉｌｉｎｅａｒｅｌｌｉｐｔｉｃｅｑｕａｉｔｏｎｓｉｎａｎｎｕｌｕｓ．ＪＤｉｆｆＥｑｎｓ，１９９４，１０９：１－７
１０　ＥｒｂｅＬＨ，ＨｕＳ，ＷａｎｇＨａｉｙａｎ．Ｍｕｌｔｉｐｌｅｐｏｓｉｔｉｖｅｓｏｌｕｔｉｏｎｓｏｆｓｏｍｅｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓ．ＪＭａｔｈＡｎａｌＡｐｐｌ，
１９９４，１８４：６４０－６４８
１１　ＭａＲｕｙｕｎ．Ｅｘｉｓｔｅｎｃｅｏｆｐｏｓｉｔｉｖｅｓｏｌｕｔｉｏｎｓｆｏｒｅｌｌｉｐｔｉｃｓｙｓｔｅｍｓ．ＪＭａｔｈＡｎａｌＡｐｐｌ，１９９６，２０１：３７５－３８６
１２　钟承奎，范先令，陈文山原．非线性泛函分析引论．兰州：兰州大学出版社，１９９８

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Existence of Positive Radial Solutions of Dirichlet Problems for Elliptic Equations Δu+g(|X|)f(u)=0 in Annulus

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