Abstract
This paper is concerned with boundary value problems of second-order impulsive differential systems on whole lines. By using Banach spaces and nonlinear operators, together with the Schauder fixed point theorem, sufficient conditions to guarantee the existence of at least one solution are established.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Agarwal, R.P.: Boundary value problems for higher order differential equations, World Scientific, Singapore (1986)
Avramescu C., Vladimirescu C.: Existence of Homoclinic solutions to a nonlinear second order ODE, Dynamics of continuous, discrete and impulsive systems. Ser. A Math. Anal. 15, 481–491 (2008)
Avramescu C., Vladimirescu C.: Existence of solutions to second order ordinary differential equations having finite limits at ±∞. Electron. J. Differ. Equ. 18, 1–12 (2004)
Avramescu C., Vladimirescu C.: Limits of solutions of a perturbed linear differential equation. Electron. J. Qual. Theory Differ. Equ. 3, 1–11 (2002)
Bianconi B., Papalini F.: Non-autonomous boundary value problems on the real line. Discret Contin. Dyn. Syst. 15, 759–776 (2006)
Cabada, A., Cid, J.A.: Heteroclinic solutions for non-autonomous boundary value problems with singular Φ-Laplacian operators, discrete continuous dynamical systems. In: Proceedings of Dynamical Systems, Differential Equations and Applications. 7th AIMS Conference, suppl., pp. 118–122 (2009)
Calamai A.: Heteroclinic solutions of boundary value problems on the real line involving singular Φ-Laplacian operators. J. Math. Anal. Appl. 378, 667–679 (2011)
Cupini G., Marcelli C., Papalini F.: On the solvability of a boundary value problem on the real line. Bound. Value Probl. 2011, 26 (2011)
Cupini G., Marcelli C. Papalini F.: Heteroclinic solutions of boundary value problems on the real line involving general nonlinear differential operators. Differ. Integral Equ. 24, 619–644 (2011)
Deimling, K.: Nonlinear Functional Analysis, Springer, Berlin (1985)
Ge, W.: Boundary Value Problems for Ordinary Differential Equations. Science Press, Beijing (2007)
Il’in V.A. Moiseev E.I.: Nonlocal boundary-value problem of the second kind for a Sturm–Liouville operator. Differ. Equ. 23, 979–987 (1987)
Lakshmikantham, V.V., Bainov, D.D., Simeonov, P.S.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)
Liu Y.: Solvability of boundary value problems for singular quasi-Laplacian differential equations on the whole line. Math. Models Anal. 17, 423–446 (2012)
Marcelli C., Papalini F.: Heteroclinic connections for fully non-linear non-autonomous second-order differential equations. J. Differ. Equ. 241, 160–183 (2007)
Philos C.G., Purnaras I.K.: A boundary value problem on the whole line to second order nonlinear differential equations. Georg. Math. J. 17, 241–252 (2010)
Rachunkova, I., Stanek, S., Tvrdy, M.: Singularities and Laplacians in boundary value problems for nonlinear ordinary differential equations. In: Drabek, P., Fonde, A. (eds.) Handbook of Differential Equations, Ordinary Differential Equations, vol. 3, pp. 606–723, Elsevier, Amsterdam (2006)
Wang Y., Ge W.: Existence of triple positive solutions for multi-point boundary value problems with a one dimensional p-Laplacian. Comput Math. Appl. 54, 793–807 (2007)
Author information
Authors and Affiliations
Corresponding author
Additional information
The first author was supported by the Natural Science Foundation of Guangdong province (No: S2011010001900) and the Guangdong Higher Education Foundation for High-level talents.
Rights and permissions
About this article
Cite this article
Liu, Y. Existence of Solutions of Boundary Value Problems for Coupled Singular Differential Equations on Whole Lines with Impulses. Mediterr. J. Math. 12, 697–716 (2015). https://doi.org/10.1007/s00009-014-0422-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00009-014-0422-1