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EXISTENCE OF SOLUTIONS FOR NON-PERIODIC superlinear SCHRDINGER EQUATIONS WITHOUT (AR) CONDITION

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Acta Mathematica Scientia 2012年第4期32卷 1559-1570页

作者：万莉莉唐春雷 School of Mathematics and Statistics Southwest UniversityChongqing 400715China School of Science Southwest University of Science and TechnologyMianyang 621010China

The existence of solutions is obtained for a class of the non-periodic SchrSdinger equation -△u ＋ V（x）u = f（x,u）, x E RN, by the generalized mountain pass theorem, where V is large at infinity and f is superline... 详细信息

关键词： Schroedinger equation superlinear generalized mountain pass theorem

MULTIPLE POSITIVE SOLUTIONS TO SINGULAR BOUNDARY VALUE PROBLEMS FOR superlinear SECOND ORDER ODES

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Acta Mathematica Scientia 2002年第2期22卷 199-206页

作者：蒋达清 Department of Mathematics Northeast Normal University Changchun 130024 China

This paper deals with the existence of positive solutions to the singular boundary value problemwhere q(t) may be singular at t = 0 and t = 1, f(t,y) may be superlinear at y =∞ and singular, at y = 0.

关键词： Singular boundary value problem existence superlinear the fixed point theorem

Existence of periodic and subharmonic solutions for second-order superlinear difference equations

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Science China Mathematics 2003年第4期46卷 506-515页

作者：郭志明庾建设 Department of Applied Mathematics Hunan University Changsha 410082China Department of MathematicsTaiyuan Normal CollegeTaiyuan 030012China Department of Applied Mathematics Hunan University Changsha 410082China

By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations. For secord-order difference equations $$\Delta ^2 x_{n - 1} + f(n, x_n ) = 0,$$ some new results are obtained for the above problems when f(t, z) has superlinear growth at zero and at infinity in z.

关键词： superlinear difference equation, periodic solution, subharmonic solution, critical point, linking.

A VARIATION OF GOLDFARB'S METHOD FOR LINEARLY CONSTRAINED OPTIMIZATIONPROBLEMS AND ITS superlinear CONVERGENCE RATE

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Systems Science and Mathematical Sciences 1998年第4期11卷 351-358页

作者： SHI Zhenjun ZHANG Yuzhong(Institute Of Operations Research, Qufu Normal University, Qse 273165, China)LI Qun(Shandong Financial College, Jinan 25000, China)

This paper presents a variant algorithm of Goldfarb’s method for linearlyconstrained optimization problems. In the variant algorithm, we introduce a concept calledconjugate projection, which differs from orthogonal p... 详细信息

关键词： Conjugate projection superlinear convergence rate global convergence

A　superlinear　CONVERGENT　FEASIBLE　METHOD　FOR　NONLINEAR　PROGRAMMING　WITH　NONLINEAR　CONSTRAINTS

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Systems Science and Mathematical Sciences 1995年第3期8卷 193-199,201-202页

作者： GAO Ziyou HE Guoping(Institute of Applied Mathematics, Academia Sinica, Beijing 100080,China)LIU Rengkui(Northern Jiaotong University, Beijing 100044, China) 中科院应用数学所北京北方交通大学北京 100044

ＡＳＵＰＥＲＬＩＮＥＡＲＣＯＮＶＥＲＧＥＮＴＦＥＡＳＩＢＬＥＭＥＴＨＯＤＦＯＲＮＯＮＬＩＮＥＡＲＰＲＯＧＲＡＭＭＩＮＧＷＩＴＨＮＯＮＬＩＮＥＡＲＣＯＮＳＴＲＡＩＮＴＳ￥ＧＡＯＺｉｙｏｕ；ＨＥＧｕｏｐｉｎｇ（Ｉｎｓｔｉ... 详细信息

ＡＳＵＰＥＲＬＩＮＥＡＲＣＯＮＶＥＲＧＥＮＴＦＥＡＳＩＢＬＥＭＥＴＨＯＤＦＯＲＮＯＮＬＩＮＥＡＲＰＲＯＧＲＡＭＭＩＮＧＷＩＴＨＮＯＮＬＩＮＥＡＲＣＯＮＳＴＲＡＩＮＴＳ￥ＧＡＯＺｉｙｏｕ；ＨＥＧｕｏｐｉｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈ...

关键词： Constrained optimization successive quadratic programming feasibility superlinear convergence.

Existence of Positive Solution for superlinear Semipositone Singular Second-order m-point Boundary Value Problem

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Chinese Quarterly Journal of Mathematics 2010年第1期25卷 151-158页

作者： ZHANG Xing-qiu School of Mathematics Liaocheng University Liaocheng 252059 China

By applying fixed point theorem, the existence of positive solution is considered for superlinear semipositone singular m-point boundary value problem -（Lφ）（x）=（p（x）φ′（x））′＋q（x）φ（x） and ξi ∈ （0,1）with 0〈ξ1〈ξ2……〈ξm-2〈1,αi ∈ R^＋,f ∈C[（0,1）×R^＋,R^＋],f（x,φ） may be singular at x=0 and x=1,g（x）：（0,1）→R is Lebesgue measurable, g may tend to negative infinity and have finitely many singularities.

关键词： semipositone superlinear singular m-point boundary value fixed point theo-rem positive solution

EXISTENCE OF POSITIVE SOLUTION TO superlinear SEMIPOSITONE SINGULAR m-POINT BOUNDARY VALUE PROBLEMS

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Annals of Differential Equations 2008年第4期24卷 490-497页

作者： Zhang Xingqiu (School of Mathematics, Liaocheng University, Liaocheng 252059, Shandong)

Sufficient conditions for the existence of positive solution to superlinear semi-positone singular m-point boundary value problem are given by cone expansion and compression theorem in norm type.

关键词： semipositone superlinear singular m-point boundary value fixed point theorem positive solution

A　superlinearLY　CONVERGENT　GENERALIZED　GRADIENT　PROJECTION　ALGORITHMFOR　LINEARLY　CONSTRAINED　PROBLEMS

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Systems Science and Mathematical Sciences 1995年第4期8卷 299-310页

作者： HE Guoping GAO Ziyou(Institute of Applied Mathematics,Academia Sinica,Beijing 100080,China)ZHU Jianqing (Zhengzhou Institute of Surveying and Mapping,Zhengzhou 450052,China) 中科院应用数学所北京解放军郑州测绘学院河南郑州 450052

Ａ　ＳＵＰＥＲＬＩＮＥＡＲＬＹＣＯＮＶＥＲＧＥＮＴＧＥＮＥＲＡＬＩＺＥＤＧＲＡＤＩＥＮＴＰＲＯＪＥＣＴＩＯＮＡＬＧＯＲＩＴＨＭＦＯＲＬＩＮＥＡＲＬＹＣＯＮＳＴＲＡＩＮＥＤ　ＰＲＯＢＬＥＭＳＮｅｗａｄｄｒｅｓｓ：Ｓｈａ... 详细信息

Ａ　ＳＵＰＥＲＬＩＮＥＡＲＬＹＣＯＮＶＥＲＧＥＮＴＧＥＮＥＲＡＬＩＺＥＤＧＲＡＤＩＥＮＴＰＲＯＪＥＣＴＩＯＮＡＬＧＯＲＩＴＨＭＦＯＲＬＩＮＥＡＲＬＹＣＯＮＳＴＲＡＩＮＥＤ　ＰＲＯＢＬＥＭＳＮｅｗａｄｄｒｅｓｓ：ＳｈａｎｄｏｎｇＭｉｎｉｎｇｉｎｓｔｉｔｕｔｅ，Ｓｈａｎｄｏｎｇ，Ｔａｉａｎ２７１０１９．＊Ｎｅｗａｄｄｒｅｓｓ：ＮｏｒｔｈｅｒｎＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔｙｌＢｅ１Ｊｉｎｇ１０００４０．ａｐｉｖｏｔｉｎｇｏｐｅｒａｔｉｏｎｉｎｏｒｄｅｒｔｏｄｅｔｅｒｍｉｎｅａｎｅ－ａｃｔｉｖｅｓｅｔｏｆｃｏｎｓｔｒａｉｎｔｓ．Ｓｅｃｏｎｄｌｙ，ｏｎｅｍｕｓｔｃｏｍｐｕｔｅａｎｅｗｐｒｏｊｅｃｔｉｏｎｍａｔｒｉｘａｔｅａｃｈｓｔｅｐ．Ｔｈｅｓｅａｒｅａｌｌｔｉｍｅ－－ｃｏｎｓｕｍｉｎｇａｎｄｏｆｔｅｎｍａｋｅｔｈｅａｌｇｏｒｉｔｈｍｔｏｂｅｕｎｓｔａｂｌｅ．ＩｎｔｈｉｓｐａｐｅｒｓｂｙｕｓｉｎｇｔｈｅｃｏｎｃｅｐｔｏｆｇｅｎｅｒａｌｉｚｅｄｐｒｏｊｅｃｔｉｏｎｍａｔｒｉＸｗｈｉｃｈｗａｓｐｒｏｐｏｓｅｄｉｎ［８］，ｗｅｉｍｐｒｏｖｅＷｕ＇ｓａｌｇｏｒｉｔｈｍａｎｄｐｒｅｓｅｎｔａｎｅｗａｌｇｏｒｉｔｈｍ．Ｕｎ?

关键词： Generalized gradient projection method linearly constrained problem superlinear convergence pivoting operation.

KAMENEV-TYPE OSCILLATION CRITERIA FOR DELAY DIFFERENCE EQUATIONS

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Acta Mathematica Scientia 2007年第3期27卷 574-580页

作者：程金发 Department of Mathematics Xiamen University

Some oscillation criteria are established by Raccati transformation techniques for the following second-order nonlinear neutral difference equation △（pn（△（Xn ＋ CnXn-τ））^γ）＋ qnX^Bn-σ = 0, n ：0, 1, 2...wh... 详细信息

关键词： Oscillation superlinear sublinear difference equations