Existence of solution for a three-point boundary value problem for a second-order impulsive differential equation

详细信息    查看全文

• 作者：Xuxin Yang (1)
  Zengyun Wang (1)
  Jianhua Shen (2)
  
  1. Department of Mathematics ; Hunan First Normal University ; Changsha聽 ; 410205 ; Hunan ; P.R. China
  2. Department of Mathematics ; Hangzhou Normal University ; Hangzhou聽 ; 310036 ; Zhejiang ; P.R. China
  
• 关键词：Boundary ; value problem ; Existence of solutions ; Ordinary differential equations with impulses ; Primary 34B10 ; Secondary 34B15
• 刊名：Journal of Applied Mathematics and Computing
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：47
• 期：1-2
• 页码：49-59
• 全文大小：205 KB
• 参考文献：1. An, Y.: Existence of solutions for a three-point boundary value problem at resonance. Nonlinear Anal. 65, 1633鈥?643 (2006) CrossRef
  2. Deiming, K.: Nonlinear Funct. Anal. Springer, Berlin (1985) CrossRef
  3. Ding, W., Ran, J., Han, M.: Periodic boundary value problems for the first order impulsive functional differential equations. Appl. Math. Comput. 165, 443鈥?56 (2005) CrossRef
  4. Franco, D., Infante, G., Zima, M.: Second order nonlocal boundary value problems at resonance. Math. Nachr. 284, 875鈥?84 (2011) CrossRef
  5. Feng, W., Webb, J.R.L.: Solvability of a three-point boundary value problems at resonance. Nonlinear Anal. 30, 3227鈥?238 (1997) CrossRef
  6. Feng, W., Webb, J.R.L.: Solvability of a m-point boundary value problems with nonlinear growth. J. Math. Anal. Appl. 212, 467鈥?80 (1997) CrossRef
  7. Gregus, M., Neumann, F., Arscott, F.M.: Three-point boundary value problems for differential equations. J. London Math. Soc. 3, 429鈥?36 (1971) CrossRef
  8. Gupta, P.C.: Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equations. J. Math. Anal. Appl. 168, 540鈥?51 (1992) CrossRef
  9. Gupta, P.C.: A sharper condition for solvability of a three-point second order boundary value problem. J. Math. Anal. Appl. 205, 586鈥?97 (1997) CrossRef
  10. He, X., Ge, W.: Triple solutions for second order three point boundary value problems. J. Math. Anal. Appl. 268, 256鈥?65 (2002) CrossRef
  11. He, Z., He, X.: Periodic boundary value problems for first order impulsive intergro-differential equations of mixed type. J. Math. Anal. Appl. 296, 8鈥?0 (2004) CrossRef
  12. Infante, G.: Eigenvalues for some non-local boundary value problems. Proc. Edinb. Math. Soc 46, 75鈥?6 (2003) CrossRef
  13. Infante, G., Zima, M.: Positive solutions of multi-point boundary value problems at resonance. Nonlinear Anal. 69, 2458鈥?465 (2008) CrossRef
  14. Liang, R., Shen, J.: Periodic boundary value problem for the first order impulsive functional differential equations. J. Comput. Appl. Math. 220, 498鈥?10 (2007) CrossRef
  15. Liu, B.: Positive solutions of a nonlinear three-point boundary value problem. Appl. Math. Comput. 132, 11鈥?8 (2002) CrossRef
  16. Ma, R.: Positive solutions of a nonlinear three-point boundary value problems. Electron. J. Differ. Equ. 34, 545鈥?55 (1999)
  17. Ma, R.: Positive solutions of a nonlinear m-point boundary value problem. Comput. Math. Appl. 42, 755鈥?65 (2001) CrossRef
  18. Ma, R.: A survey on nonlocal boundary value problems. Appl. Math. E-Notes 7, 257鈥?79 (2007)
  19. Pietramala, P.: A note on a beam equation with nonlinear boundary conditions, Bound. Value Probl. 2011 (2011), Art. ID 376782, 14 pp
  20. Webb, J.R.L., Infante, G.: Positive solutions of nonlocal boundary value problems: a unified approach. J. Lond. Math. Soc. 74, 673鈥?93 (2006) CrossRef
  21. Webb, J.R.L., Zima, M.: Multiple positive solutions of resonant and nonresonant nonlocal boundary value problems. Nonlinear Anal. 71, 1369鈥?378 (2009) CrossRef
  22. Sun, Y.P.: Nontrivial solution for a three-point boundary-value problem. Electron. J. Differ. Equ. 111, 1鈥?0 (2004)
  23. Timoshenko, S.: Theory elastic stability. McGraw-Hill, New York (1961)
  24. Zhang, P.: Existence of positive solutions for nonlocal second-order boundary value problem with variable parameter in Banach spaces. Fixed Point Theory Appl. 2011, 43 (2011) CrossRef
  25. Zhang, H.E., Sun, J.P.: Positive solutions of third-order nonlocal boundary value problems at resonance. Boundary value problems 2012, 102 (2012) CrossRef
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Computational Mathematics and Numerical Analysis
  Applied Mathematics and Computational Methods of Engineering
  Theory of Computation
  Mathematics of Computing
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1865-2085

文摘

In this paper, we study the existence of nontrivial solutions for the second-order three-point boundary value problem with impulses. Under certain growth conditions on the nonlinearity function and by using Leray-Schauder nonlinear alternative, sufficient conditions for the existence of a nontrivial solution are obtained. Furthermore, we illustrate our results with some examples.