四阶非线性常微分方程非线性三点边值问题解的存在性与唯一性

Abstract

Abstract:

In this paper,by using the “Matching” technique, gives concrete sufficient conditions of the existence and uniqueness of solutions of nonlinear three-point boundary value problems for fourth order nonlinear ordinary differential equation

Y⁽⁴⁾ = f(x, y, y′,y″,y⁽³⁾),

with the nonlinear threepoint boundary conditions

k(y(b),y′(b),y″(b),y⁽³⁾(b),y(a),y′(a),y″(a),y⁽³⁾(a))=0,

y(b)=μ

g(y′(b),y⁽³⁾(b))=0,

h(y(b),y′(b),y″(b),y⁽³⁾(b),y(c),y′(c),y″(c),y⁽³⁾(c))=0

Key words: Ｆｏｕｒｔｈｏｒｄｅｒｎｏｎｌｉｎｅａｒｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ, Ｔｈｒｅｅｐｏｉｎｔｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓ, Ｅｘｉｓｔｅｎｃｅ, Ｕｎｉｑｕｅｎｅｓｓ．

CLC Number:

３４Ｂ１５

Pei Minghe Yu Hailan. Existence and Uniqueness of Solutions of Nonlinear Three-Point Boundary Value Problems for Fourth Order Nonlinear Ordinary Differential Equations[J].Acta mathematica scientia,Series A, 2000, 20(2): 194-201.

Trendmd

References

１　ＵｓｍａｎｉＲＡ．Ａｕｎｉｑｕｅｎｅｓｓｔｈｅｏｒｅｍｆｏｒａｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍ．ＰｒｏｃＡｍｅｒＭａｔｈＳｏｃ，１９７９，７７：３２７－３３５
２　ＹａｎｇＹ．ＦｏｕｒｔｈｏｒｄｅｒｔｗｏｐｏｉｎｔＢｏｕｎｄａｒｙｐｒｏｂｌｅｍｓ．ＰｒｏｃＡｍｅｒＭａｔｈＳｏｃ，１９８８，１０４：１７５－１８０
３　ＡｆｔａｄｉｚａｄｅｈＡＲ．Ｅｘｉｓｔｅｎｃｅａｎｄｕｎｉｑｕｅｎｅｓｓｔｈｅｏｒｅｍｓｆｏｒｆｏｕｒｔｈｏｒｄｅｒｂｏｕｎｄａｒｙｐｒｏｂｌｅｍｓ．ＪＭａｔｈＡｎａｌＡｐｐｌ，１９８６，１１６：４１５－４２６
４　ＧｕｐｔａＣＰ．Ｅｘｉｓｔｅｎｃｅａｎｄｕｎｉｑｕｅｎｅｓｓｔｈｅｏｒｅｍｓｆｏｒｔｈｅｂｅｎｄｉｎｇｏｆａｎｅｌａｓｔｉｃｂｅａｍｅｑｕａｔｉｏｎ．ＡｐｐｌｉｃａｂｌｅＡｎａｌｙｓｉｓ，１９８８，２６：２８９－３０４
５　ＨｅｎｄｅｒｓｏｎＪ，ＭｃｇｗｉｅｒＲ．Ｕｎｉｑｕｅｎｅｓｓ，ｅｘｉｓｔｅｎｃｅ，ａｎｄｏｐｔｉｍａｌｉｔｙｆｏｒｆｏｕｒｔｈｏｒｄｅｒＬｉｐｓｃｈｉｔｚｅｑｕａｔｉｏｎｓ．ＪＤｉｆｆＥｑｕｓ，１９８７，６７：４１４－４４０
６　ＤｅｌｐｉｎｏＭＡ，ＭａｎａｓｅｖｉｃｈＲＦ．Ｅｘｉｓｔｅｎｃｅｆｏｒａｆｏｕｒｔｈｏｒｄｅｒｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｕｎｄｅｒａｔｗｏｐａｒａｍｅｔｅｒｎｏｎｒｅｓｏｎａｎｃｅｃｏｎｄｉｔｉｏｎ．ＰｒｏｃＡｍｅｒＭａｔｈＳｏｃ，１９９１，１１２：８１－８７
７　裴明鹤．四阶非线性常微分方程非线性两点边值问题解的存在唯一性．高校应用数学学报，１９９５，１０犃（３）：２８５－２９４
８　高永馨．非线性四阶常微分方程三点边值问题解的存在性．应用数学和力学，１９９６，１７：５４３－５５０
９　ＭｏｏｒｔｉＶＲＧ，ＧａｒｍｅｒＪＢ．Ｅｘｉｓｔｅｎｃｅｕｎｉｑｕｅｎｅｓｓｔｈｅｏｒｅｍｓｆｏｒｔｈｒｅｅｐｏｉｎｔｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓｆｏｒｎｔｈｏｒｄｅｒｎｏｎｌｉｎｅａｒｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ．ＪＤｉｆｆＥｑｕｓ，１９７８，２９：２０５－２１３
１０　ＨａｒｔｍａｎＰ．ＯｒｄｉｎａｒｙＤｉｆｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎｓ．ＮｅｗＹｏｒｋ：Ｗｉｌｅｙ，１９６４

[1]	Wang Jun, Wang Tianlu, Wen Yanhua, Zhou Xianfeng. Global Solutions of IVP for N-Dimensional Nonlinear Fractional Differential Equations with Delay [J]. Acta mathematica scientia,Series A, 2018, 38(5): 903-910.
[2]	Xing Chao, Ren Mengzhang, Luo Hong. The Existence of Global Weak Solutions to Thermohaline Circulation Equations [J]. Acta mathematica scientia,Series A, 2018, 38(2): 284-290.
[3]	Zhang Shuqin, Hu Lei. Initial Value Problem for Nonlinear Fractional Differential Equations with Variable-order Derivative and a Parameter [J]. Acta mathematica scientia,Series A, 2018, 38(2): 291-303.
[4]	Zhu Xincai. Existence of Constrained Minimizers for Schrödinger-Poisson Equations in R^N [J]. Acta mathematica scientia,Series A, 2018, 38(1): 61-70.
[5]	Su Xiao, Wang Shubin. Finite Time Blow-Up for the Damped Semilinear Wave Equations with Arbitrary Positive Initial Energy [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1085-1093.
[6]	Li Qin, Yang Zuodong. Infinitely Many High Energy Solutions of p-Kirchhoff-Type System with Sign-Changing Weight [J]. Acta mathematica scientia,Series A, 2017, 37(5): 869-876.
[7]	Li Qingwei, Gao Wenjie, Han Yuzhu. Existence of Solutions to Some Singular Elliptic Problems with Degenerate Coercivity [J]. Acta mathematica scientia,Series A, 2017, 37(5): 877-894.
[8]	Huang Decheng, Chen Shouxin. New Proof for the Existence of Minimizing Energy Solutions for the Ginzburg-Landau Equations [J]. Acta mathematica scientia,Series A, 2017, 37(2): 299-306.
[9]	Qiu Hua, Zhang Yingshu, Fang Shaomei. The Global Existence Result of a Leray-α-Oldroyd Model to the Incompressible Viscoelastic Flow [J]. Acta mathematica scientia,Series A, 2017, 37(1): 102-112.
[10]	Yuan Hailong, Li Yanling. Existence and Stability of Coexistence States for a Lotka-Volterra Competition Model [J]. Acta mathematica scientia,Series A, 2017, 37(1): 173-184.
[11]	Zhang Hongwei, Liu Gongwei, Hu Qingying. Initial Boundary Value Problem for a Class Wave Equation with Logarithmic Source Term [J]. Acta mathematica scientia,Series A, 2016, 36(6): 1124-1136.
[12]	Liu Yang. Potential Well and Application to Non-Newtonian Filtration Equations at Critical Initial Energy Level [J]. Acta mathematica scientia,Series A, 2016, 36(6): 1211-1220.
[13]	Huang Shoujun, Wang Rui. Plane Wave Solutions to the Euler Equations for Chaplygin Gases [J]. Acta mathematica scientia,Series A, 2016, 36(4): 681-689.
[14]	Yao Qingliu. Existence and Successively Iterative Method of Singular Solution to a Nonlinear Fractional Differential Equation [J]. Acta mathematica scientia,Series A, 2016, 36(2): 287-296.
[15]	Li Qin, Yang Zuodong. Multiple Solutions for a Class of Quasilinear Nonhomogeneous Elliptic Systems with Nonlinear Boundary Conditions [J]. Acta mathematica scientia,Series A, 2016, 36(2): 307-316.

Existence and Uniqueness of Solutions of Nonlinear Three-Point Boundary Value Problems for Fourth Order Nonlinear Ordinary Differential Equations

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10