Solutions of two-point BVPs at resonance for higher order impulsive differential equations

Nonlinear Analysis, Theory, Methods and Applications

Volumn 60, Issue 5, 2005, Pages 887-923

  Liu, Yuji ^a,b   Yang, Pinghua ^a   Ge, Weigao ^a  

^a BEIJING INSTITUTE OF TECHNOLOGY   (China)

^b HUNAN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Fixed point theorem; Higher order differential equation; Resonance; Solution; Two point boundary value problem

Indexed keywords

BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

FIXED POINT THEOREM; HIGHER-ORDER DIFFERENTIAL EQUATION; SOLUTION; TWO-POINT BOUNDARY VALUE PROBLEM;

RESONANCE;

EID: 12444305348     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.09.054     Document Type: Article

References (31)

1. R.P. Agarwal, D. O'Regan, and P.J.Y. Wong Positive Solutions of Differential, Difference and Integral Equations 1999 Kluwer Academic Publishers Dordrecht
2. R.I. Avery, J.M. Davis, J. Henderson, Three symmetric positive solutions for Lidstone-Williams theorem, Electronic J. Diff. Equ. 2000 (2000) No. 40, 1-15.
3. D.D. Bainov, and P.S. Simeonov Impulsive Differential Equations Periodic Solutions and Applications 1993 Longnan Harlow
4. C.J. Chyan, and J. Henderson Positive solutions of 2mth-order boundary value problems Appl. Math. Lett. 15 2002 767 774
5. P.E. Eloe, J. Henderson, and H.B. Thompson Extremal points for impulsive Lidstone boundary value problems Math. Comput. Modelling 32 2000 687 698
6. W. Feng, and J.R.L. Webb Solvability of m-point boundary value problems with nonlinear growth J. Math. Anal. Appl. 212 1997 467 489
7. R.E. Gaines, J.L. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Lecture Notes in Mathematics, vol. 568, Springer, Berlin, 1977.
8. J.R. Graef, and B. Yang On a nonlinear boundary value problem for fourth-order differential equations Appl. Anal. 72 1999 439 448
9. J.R. Graef, and B. Yang Existence and non-existence of positive solutions of fourth-order nonlinear boundary-value problems Appl. Anal. 74 2000 201 214
10. D. Guo Multiple positive solutions of impulsive nonlinear Fredholm integral equations and applications J. Math. Anal. Appl. 173 1993 318 324
11. D. Guo Nonlinear impulsive Volterra integral equations in Banach spaces and applications J. Appl. Math. Stochastic Anal. 6 1993 35 48
12. D. Guo Existence of solutions of boundary value problems for second order impulsive differential equations in Banach spaces J. Math. Anal. Appl. 181 1994 407 421
13. C.P. Gupta Existence and uniqueness theorems for bending of an elastic beam equation Appl. Anal. 26 1988 298 304
14. C.P. Gupta A nonlinear boundary value problem associated with the elastic equilibrium of an elastic beam supported by sliding clamps J. Math. Sci. 12 1989 697 712
15. P. Gupta, J.J. Nieto, and L. Sanchez Periodic solutions of some Lienard and Duffine equations J.Math. Anal. Appl. 140 1989 67 82
16. C.P. Gupta, S.K. Ntougas, and P.C. Tsamatos Solvability of an m-point boundary value problem for second order ordinary differential equations J. Math. Anal. Appl. 189 1995 575 584
17. J. Henderson, and H.B. Thompson Smoothness of solutions for boundary value problems with impulse effects, (II) Math. Comput. Modelling 23 10 1996 61 69
18. V. Il'in, and E. Moiseev Non-local boundary value problems of first kind for a Sturm-Liouville operator in its differential and finite difference aspects Differential Eqns. 23 1987 803 810
19. I.T. Kigaradze, and T. Kusanno Periodic solutions of nonautonomous ordinary differential equations of higher order Differential Equations 35 1 1999 70 77
20. V. Lakshmikantham, D.D. Bainov, and P. Simenov Theory of Impulsive Differential Equations 1989 World Scientific Singapore
21. B. Liu Solvability of multi-point boundary value problems at resonance (III) Appl. Math. Comput. 129 2002 119 143
22. B. Liu Solvability of multi-point boundary value problems at resonance (IV) Appl. Math. Comput. 143 2003 275 299
23. Y. Liu, and W. Ge Double positive solutions of fourth-order nonlinear boundary value problems Appl. Anal. 82 4 2002 369 380
24. Y. Liu, W. Ge, Solvability of two-point boundary value problems for fourth-order differential equations at resonance, J. Anal. Appl. (Zeitschrift Fur Analysis und Ihre Anwendungen) 22 (2003) 977-989.
25. B. Liu, and J. Yu Solvability of multi-point boundary value problems at resonance (I) India J. Pure Appl. Math. 33 4 2002 475 494
26. B. Liu, and J. Yu Existence of solutions for m-point boundary value problems of second order differential systems with impulses Appl. Math. Comput. 125 2002 155 175
27. B. Liu, and J. Yu Solvability of multi-point boundary value problems at resonance (II) Appl. Math. Comput. 136 2003 353 377
28. R. Ma, and H. Wang On the existence of positive solutions of fourth-order differential equations Appl. Anal. 59 1995 225 231
29. R. Ma, J. Zhang, and S. Fu The method of lower and upper solutions for fourth order two-point boundary value problems J. Math. Anal. Appl. 215 1997 415 422
30. P.K. Palamides Positive solutions for higher-order Lidstone boundary value problems a new approach Via Sperner's Lemma Comput. Math. Appl. 42 2001 75 89
31. X. Yang Upper and lower solutions for periodic solutions Appl. Math. Comput. 137 2003 413 422