Positive Solutions of Boundary Value Problem for a Coupled System of Nonlinear Third-order Differential Equations
Positive Solutions of Boundary Value Problem for a Coupled System of Nonlinear Third-order Differential Equations
摘要
By using cone expansion-compression theorem in this paper, we study boundary value problems for a coupled system of nonlinear third-order differential equation. Some sufficient conditions are obtained which guarantee the boundary value problems for a coupled system of nonlinear third-order differential equation has at least one positive solution. Some examples are given to verify our results.
基金
Foundation item： Supported by the National Natural Science Foundation of China（10801001）
Supported by the Natural Science Foundation of Anhui Province（1208085MA13）
参考文献14
-
1MA :Ru-yun. Multiplicity of positive solutions for second-order three-point boundary value problems[J] Computers Mathematics with Applications, 2000, 40: 193-204.
-
2YAO Qing-liu. Existence and multiplicity of positive solutions for a class of second-order three-point non- linear boundary value problems[J]. Acta Mathematica Sinica, 2002, 6: 1057-1064.
-
3LIU Bing. Positive solutions of a nonlinear three-point boundary value problem[J]. Applied Mathematics Com-putation, 2002, 132: 11-28.
-
4MA Ru-yun. Positive solutions of a nonlinear three-point boundary value problem[J]. Electronic Journal of Differential Equations, 1998, 34: 1-8.
-
5ERBE L H, WANG H Y. On the existence of positive solutions of ordinary differential equations[J]. Proe Amer Math Soc, 1994, 120: 743-748.
-
6SUN Yong-ping. Positive solutions for third-order three-point nonhomogeneous boundary value problems[J]. Appl Math Lett, 2009, 22: 45-51.
-
7XIE Sheng-li, ZHU Jiang. Existence of positive radial solutions for elliplic systems[J]. Advance in Dy- namical Systems and Applications, 2007, 2(1): 123-133.
-
8GE Wei-gao. Boundary Value Problem of Nonlinear Ordinary Differential Equation[M]. Beijing: Science Press, 2007.
-
9MA Ru-yun. Non-local Problems of Nonlinear Ordinary Differential Equation[M]. Beijing: Science Press, 2004.
-
10YANG Zhi-lin. Positive solutions of boundary value problems for systems of nonlinear second ordinary differential equations[J]. Acta Math Sinica, 2004, 47(1): 111-118.
二级参考文献10
-
1MA Ru-yun. Non-local Problems of Nonlinear Ordinary Differential Equation[M]. Beijing: Science Press, 2004.
-
2GUO Da-jun. Nonlinear Function Analysis[M]. Jinan" Science and Technology Press, 2004.
-
3GE Wei-gao. Boundary Value Problem of Nonlinear Ordinary Differential Equation[M]. Beijing: Science Press, 2007.
-
4HU Ling, "WANG Liang-long. Multiple positive solutions of boundary value problem for systems of nonlinear second-order differential equations[J]. Math Anal Appl, 2007, 335: 1052-1060.
-
5XIE Sheng-li, ZHU Jiang. Existence of positive radial solutions for elliplic systems[J]. Advance in Dynamical Systems and Applications, 2007, 2(1): 123-133.
-
6MA Ru-yun. Existence of positive radial solutions for elliplic systems[J]. Math Anal Appl, 1996, 201(2): 375-386.
-
7YANG Zhi-lin. Positive solutions of boundary value problems for systems of nonlinear second ordinary differential equations[J]. Acta Math Sinica, 2004, 47(1): 111-118.
-
8YANG Zhi-lin. Positive solutions to a system of second-order nonlocat boundary value problems[J]. Nonlinear Anal, 2005, 62(7): 1251-1265.
-
9ERBE L H,WANG Hai-yan. On the existence of positive solutions of ordinary differential equations[J]. Proe Amer Math Soc, 1994, 120: 743-748.
-
10DUNNINGER D K, WANG Hai-yan. Multiplicity of positive solutions for an elliptic system on an annulus[J]. Nonlinear Analysis, 2000, 42: 80.
-
1LORNA S. ALMOCERA,POLLY W. SY,井竹君.HOPF BIFURCATION AND ANALYSIS OF EQUILIBRIUM FOR A THIRD-ORDER DIFFERENTIAL EQUATION IN A MODEL OF COMPETITION[J].Acta Mathematicae Applicatae Sinica,2001,17(1):68-80.
-
2Yaohong LI,Xiaoyan ZHANG.Multiple Positive Solutions of Boundary Value Problems for Systems of Nonlinear Third-Order Differential Equations[J].Journal of Mathematical Research with Applications,2013,33(3):321-329. 被引量：2
-
3莫嘉琪,温朝晖.A class of boundary value problems for third-order differential equation with a turning point[J].Applied Mathematics and Mechanics(English Edition),2010,31(8):1027-1032.
-
4Amar Makhlouf,Meriem Hamamda.LIMIT CYCLES OF THIRD-ORDER DIFFERENTIAL EQUATION[J].Annals of Differential Equations,2014,30(4):416-423.
-
5Kemei Zhang, Wei Wang (Dept. of Math., Qufu Normal University, Qufu 273165, Shandong).POSITIVE SOLUTIONS TO PERIODIC BOUNDARY VALUE PROBLEM OF SINGULAR SEMI-POSITONE NONLINEAR THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS[J].Annals of Differential Equations,2010,26(3):359-367. 被引量：1
-
6马善钧,葛卫国,黄沛天.The third-order Lagrange equation for mechanical systems of variable mass[J].Chinese Physics B,2005,14(5):879-881. 被引量：6
