Impulsive BVPs with nonlinear boundary conditions for the second order differential equations without growth restrictions

Journal of Mathematical Analysis and Applications

Volumn 292, Issue 2, 2004, Pages 525-539

  Rachůnková, Irena ^a   Tomeček, Jan ^a  

^a PALACKÝ UNIVERSITY   (Czech Republic)

Author keywords

Impulses; Lower and upper functions; Nonlinear boundary value conditions; Ordinary differential equation of the second order

Indexed keywords

EID: 11144357008     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2003.12.023     Document Type: Article

References (19)

1. D. Bainov, P. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, in: Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 66, Longman, Harlow, 1993.
2. A. Cabada, J.J. Nieto, D. Franco, S.I. Trofimchuk, A generalization of the monotone method for second order periodic boundary value problem with impulses at fixed points, Dynam. Contin. Discrete Impuls. Systems 7 (2000) 145-158.
3. Y. Dong, Periodic solutions for second order impulsive differential systems, Nonlinear Anal. 27 (1996) 811-820.
4. L.H. Erbe, X. Liu, Existence results for boundary value problems of second order impulsive differential equations, J. Math. Anal. Appl. 149 (1990) 56-69.
5. R.E. Gaines, J. Mawhin, Coincidence Degree and Nonlinear Differential Equations, in: Lecture Notes in Mathematics, vol. 568, Springer-Verlag, Berlin, 1977.
6. A. Granas, R.B. Guenther, J.W. Lee, Some general existence principles in the Carathéodory theory of non-linear differential systems, J. Math. Pures Appl. 70 (1991) 153-196.
7. S. Hu, V. Lakshmikantham, Periodic boundary value problems for second order impulsive differential systems, Nonlinear Anal. 13 (1989) 75-85.
8. A. Lepin, L. Lepin, Boundary Value Problems for Ordinary Differential Equations of the Second Order, Zinatne, Riga, 1988 (in Russian).
9. V. Lakshmikantham, D. Bainov, P. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
10. E. Liz, Existence and approximation of solutions for impulsive first order problems with nonlinear conditions, Nonlinear Anal. 25 (1995) 1191-1198.
11. E. Liz, J.J. Nieto, Periodic solutions of discontinuous impulsive differential systems, J. Math. Anal. Appl. 161 (1991) 388-394.
12. E. Liz, J.J. Nieto, The monotone iterative technique for periodic boundary value problems of second order impulsive differential equations, Comment. Math. Univ. Carolin. 34 (1993) 405-411.
13. I. Rachůnková, Upper and lower solutions and topological degree, J. Math. Anal. Appl. 234 (1999) 311-327.
14. I. Rachůnková, Upper and lower solutions and multiplicity results, J. Math. Anal. Appl. 246 (2000) 449-464.
15. I. Rachůnková, J. Tomeček, On nonlinear boundary value problems with impulses, Math. Notes 3 (2002) 59-69.
16. I. Rachůnková, J. Tomeček, On nonlinear boundary value problems for systems of differential equations with impulses, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 41 (2002) 119-129.
17. I. Rachůnková, M. Tvrdý, Nonmonotone impulse effects in second order periodic boundary value problems, Funct. Differential Equations 9 (2002) 471-498.
18. A.M. Samoilenko, N.A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.
19. Z. Zhang, Existence of solutions for second order impulsive differential equations, Appl. Math. Ser. B (English Ed.) 12 (1997) 307-320.