Abstract
This paper is concerned with the existence of positive solutions of second-order impulsive boundary value problem with integral boundary conditions on time scales. Existence results of at least three positive solutions are established via a new fixed point theorem in a cone. Also, an example is given to illustrate the effectiveness of our result.
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Agarwal R.P., Bohner M.: Basic calculus on time scales and some of its applications. Result Math. 35, 3–22 (1999)
Akhmet M.: Principles of Discontinuous Dynamical Systems. Springer, New York (2010)
Anderson D.R., Karaca I.Y.: Higher-order three-point boundary value problem on time scales. Comput. Math. Appl. 56, 2429–2443 (2008)
Bohner, M., Peterson, A.: Dynamic Equations on Time Scales: An Introduction with Applications. Birkhäuser, Boston (2001)
Bohner M., Peterson, A.: Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston (2003)
Boucherif A.: Second-order boundary value problems with integral boundary conditions. Nonlinear Anal. 70, 364–371 (2009)
Chen H., Wang H.: Triple positive solutions of boundary value problems for p-Laplacian impulsive dynamic equations on time scales. Math. Comput. Model 47, 917–924 (2008)
Cui X.Y., Shi X.Y.: Existence of solutions for first-order impulsive dynamic equations on time scales with integral boundary conditions. Math. Pract. Theory 42, 193–198 (2012)
Guo D.J., Liu X.Z.: Multiple positive solutions of boundary-value problems for impulsive differential equations. Nonlinear Anal. 25, 327–337 (1995)
Graef J.R., Ouahab A.: Some existence results for impulsive dynamic equations on time scales with integral boundary conditions. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 13, 11–24 (2006)
Hilger, S.: Ein Maßkettenkalkül mit Anwendug auf Zentrumsmanningfaltigkeiten. Ph.D. Thesis, Universität Würzburg (1988)
Hu L., Liu L., Wu Y.: Positive solutions of nonlinear singular two-point boundary value problems for second-order impulsive differential equations. Appl. Math. Comput. 196, 550–562 (2008)
Hu M., Wang L.: Triple positive solutions for an impulsive dynamic equation with integral boundary condition on time scales. Int. J. Appl. Math. Stat. 31, 67–78 (2013)
Karaca I.Y.: On positive solutions for fourth-order boundary value problem with impulse. J. Comput. Appl. Math. 225, 356–364 (2009)
Karaca I.Y.: Positive solutions for boundary value problems of second-order functional dynamic equations on time scales. Adv. Difference Equ. Art. ID 829735, 21 (2009)
Lakshmikantham, V., Sivasundaram S., Kaymakcalan, B.: Dynamic Systems on Measure Chains. Kluwer, Dordrecht (1996)
Li Y., Shu, J.: Multiple positive solutions for first-order impulsive integral boundary value problems on time scales. Bound. Value Probl. 2011(12), 19 (2011)
Liang J., Liu J.H., Xiao T.J.: Nonlocal impulsive problems for nonlinear differential equations in Banach spaces. Math. Comput. Modelling 49, 798–804 (2009)
Lv Z.W., Liang J., Xiao T.J.: Multiple positive solutions for second order impulsive boundary value problems in Banach spaces. Electron. J. Qual. Theory Differ. Equ. 38, 1–15 (2010)
Ren J.L., Ge W., Ren B.X.: Existence of three positive solutions for quasi-linear boundary value problem. Acta Math. Appl. Sin. Engl. Ser. 21, 353–358 (2005)
Samoilenko, A.M., Perestyuk, N.A.: Impulsive Differential Equations. World Scientific, Singapore (1995)
Zhao A., Bai Z.: Existence of solutions to first-order impulsive periodic boundary value problems. Nonlinear Anal. 71, 1970–1977 (2009)
Zhang X., Feng M., Ge W.: Existence results for nonlinear boundary-value problems with integral boundary conditions in Banach spaces. Nonlinear Anal. 69, 3310–3321 (2008)
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Fen, F.T., Karaca, I.Y. Existence of Positive Solutions for Nonlinear Second-Order Impulsive Boundary Value Problems on Time Scales. Mediterr. J. Math. 13, 191–204 (2016). https://doi.org/10.1007/s00009-014-0494-y
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DOI: https://doi.org/10.1007/s00009-014-0494-y