Acta mathematica scientia,Series A ›› 2000, Vol. 20 ›› Issue (4): 433-444.
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Abstract:
In this paper, we discuss one class of nonlinear Schrodinger equations with periodical and sign-changing potentials. We use the Lyapunov-Schmidt reduction method and concentrationcompactness principle to get the existence of a weak solution. Key words Schrodinger operators, Concentration compactness, Periodical and sign-changing potentials.
Key words: Schrodinger operators, Concentration compactness, Periodical and sign-changing potentials.
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Liu Xiaochun. An Existence Theroem on a Class of Nonlinear Schrodinger Equations with Periodical and Sign-Changing Potentials Liu Xiaochun[J].Acta mathematica scientia,Series A, 2000, 20(4): 433-444.
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http://121.43.60.238/sxwlxbA/EN/Y2000/V20/I4/433
１ ＡｌａｍａＳ，ＴａｒｅｎｔｅｌｌｏＧ．Ｏｎｓｅｍｉｌｉｎｅａｒｅｌｌｉｐｔｉｃｅｑｕａｔｉｏｎｓｗｉｔｈｉｎｄｅｆｉｎｉｔｅｎｏｎｌｉｎｅａｒｉｔｉeｓ．ＣａｌｃＶａｒ，１９９３，１：４３９－４７５ ２ ＢｕｆｆｏｎｉＢ，ＪｅａｎｊｅａｎＬ．Ｂｉｆｕｒｃａｔｉｏｎｆｒｏｍｔｈｅｓｐｅｃｔｒｕｍｔｏｗａｒｄｓｒｅｇｕｌａｒｖａｌｕｅｓ．ＪＲｅｉｎｅＡｎｇｅｗ Ｍａｔｈ，１９９３，４４５：１－２９ ３ ＢｕｆｆｏｎｉＢ，ＪｅａｎｊｅａｎＬ．Ｍｉｎｉｍａｘｃｈａｒａｃｔｅｒｉｚａｔｉｏｎｏｆｓｏｌｕｔｉｏｎｓｆｏｒａｓｅｍｉｌｉｎｅａｒｅｌｌｉｐｔｉｃｅｑｕａｔｉｏｎｗｉｔｈｌａｃｋｏｆｃｏｍｐａｃｔｎｅｓｓ．ＡｎｎＩｎｓｔＨ ＰｏｉｎｃａｒｅＡｎａｌ，１９９３，１０（４）：３７７－４０４ ４ ＣｈｏｗＳＮ，ＨａｌｅＪＫ．Ｍｅｔｈｏｄｓｏｆｂｉｆｕｒｃａｔｉｏｎｔｈｅｏｒｙ．ＢｅｒＨｅｉｄＮｅｗ Ｙｏｒｋ，１９８２ ５ ＥｋｅｌａｎｄＩ．Ｏｎｔｈｅｖａｒｉａｔｉｏｎａｌｐｒｉｎｃｉｐｌｅ．ＪＭａｔｈＡｎａｌＡｐｐｌ，１９７４，４７：３２４－３５２ ６ ＨａｎｓＰｅｔｅｒＨｅｉｎｚ．Ｅｘｉｓｔｅｎｃｅａｎｄｇａｐｂｉｆｕｒｃａｔｉｏｎｏｆｍｕｌｔｉｐｌｅｓｏｌｕｔｉｏｎｓｔｏｃｅｒｔａｉｎｎｏｎｌｉｎｅａｒｅｉｇｅｎｖａｌｕｅｐｒｏｂｌｅｍｓ．ＮｏｎＡｎａｌＴ Ｍ Ａ，１９９３，２１（６）：４５７－４８４ ７ ＬｉｏｎｓＰＬ．ＴｈｅｃｏｎｃｅｎｔｒａｔｉｏｎｃｏｍｐａｃｔｎｅｓｓｐｒｉｎｃｉｐｌｅｉｎｔｈｅｃａｌｃｕｌｕｓｏｆｖａｒｉａｔｉｏｎｓＰａｒｔ１．ＡｎｎＩｎｓｔＨ ＰｏｉｎｃａｒｅＡｎａｌ，１９８４，１：１０９－１４５ ８ ＬｉｏｎｓＰＬ．ＴｈｅｃｏｎｃｅｎｔｒａｔｉｏｎｃｏｍｐａｃｔｎｅｓｓｐｒｉｎｃｉｐｌｅｉｎｔｈｅｃａｌｃｕｌｕｓｏｆｖａｒｉａｔｉｏｎｓＰａｒｔ１．ＡｎｎＩｎｓｔＨ ＰｏｉｎｃａｒｅＡｎａｌ，１９８４，１：２２３－２８３ ９ ＬｉｏｎｓＪＬ，ＭａｇｅｎｅｓＥ．ＮｏｎｈｏｍｏｇｅｎｅｏｕｓｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓａｎｄａｐｐｌｉｃａｔｉｏｎｓＩ．ＳｐｒｉｎｇｅｒＶｅｒｌａｇ，１９７２ １０ ＺｈｕＸＰ，ＺｈｏｕＨＳ．Ｂｉｆｕｒｃａｔｉｏｎｆｒｏｍｔｈｅｅｓｓｅｎｔｉａｌｓｐｅｃｔｒｕｍｏｆｓｕｐｅｒｌｉｎｅａｒｅｌｌｉｐｔｉｃｅｑｕａｔｉｏｎｓ．ＡｐｐｌＡｎａｌ，１９８８，２８：５１-６６ １１ 刘晓春．具凹凸性混合的非线性Ｓｃｈｒ¨ｏｄｉｎｇｅｒ方程的解的存在性定理．南昌大学学报（自科版），１９９８，（１）：３１－３９
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