Existence of positive solutions to impulsive nonlinear differential systems of second order with two-point boundary conditions
DOI:
https://doi.org/10.24193/subbmath.2024.3.10Keywords:
Two-point boundary values problems, impulsive problems, Krasnosel’skii’s fixed point theorem, positive solutionsAbstract
In this paper the authors consider the existence of positive solutions to a two point boundary value problem for nonlinear second-order impulsive systems. They use a vector version of Krasnosel’ skii’s fixed point theorem in cones in their proofs. Examples are provided to illustrate the results.
Mathematics Subject Classification (2010): 47H10, 47H07, 34B18, 34C25.
Received 01 August 2022; Accepted 16 January 2023.
References
Abdeli, H., Graef, J.R., Kadari, H., Ouahab, A., Oumansour, A., Existence of solutions to systems of second-order impulsive differential equation with integral boundary condition on the half-line, Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal., 29 (2022), 91–209.
Berrezoug, H., Henderson, J., Ouahab, A., Existence and uniqueness of solutions for a system of impulsive differential equations on the half-line, J. Nonlinear. Funct. Anal., 2017(2017), Art. ID 38, 1–16.
Bolojan-Nica, O., Infante, G., Pietramala, P., Existence results for impulsive systems with initial nonlocal conditions, Math. Model. Anal., 18(2013), 599–611.
Djebali, S., Moussaoui, T., Precup, R., Fourth-order p-Laplacian nonlinear systems via the vector version of Krasnosel’skii’s fixed point theorem, Mediterr. J. Math., 6(2009), 447–460.
Graef, J.R., Henderson, J., Ouahab, A., Topological Methods for Differential Equations and Inclusions, Monographs and Research Notes in Mathematics, CRC Press, Boca Raton, 2019.
Graef, J.R., Kadari, H., Ouahab, A., Oumansour, A., Existence results for systems of second-order impulsive differential equations, Acta Math. Univ. Comenian. (N.S.), 88(2019), 51–66.
He, Y., Existence of positive solutions to second-order periodic boundary value problems with impulse actions, Theoretical Math. Appl., 4(2014), 79–91.
Herlea, D., Existence and localization of positive solutions to first order differential systems with nonlocal conditions, Stud. Univ. Babeș-Bolyai Math., 59(2014), no. 2, 221–231.
Lin, X., Jiang, D., Multiple positive solutions of Dirichlet boundary value problems for second order impulsive differential equations, J. Math. Anal. Appl., 321(2006), 501–514.
Liu, L., Hu, L., Wu, Y., Positive solutions of nonlinear singular two-point boundary value problems for second-order impulsive differential equations, App. Math. Comput., 196(2008), 550–562.
Liu, L., Hu, L., Wu, Y., Positive solutions of two-point boundary value problems for systems of nonlinear second-order singular and impulsive differential equations, Nonlinear Anal., 69(2008), 3774–3789.
Liu, X., Li, Y., Positive solutions for Neumann boundary value problems of second-order impulsive differential equations in Banach spaces, Abstract Appl. Anal., 2012(2012), Art. ID 401923, 1–14.
Precup, R., A vector version of Krasnosel’skii’s fixed point theorem in cones and positive periodic solutions of nonlinear systems, J. Fixed Point Theory Appl., 2(2007), 141–151.
Precup, R., Positive solutions of nonlinear systems via the vector version of Krasnosel’skii’s fixed point theorem in cones, Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity, 5(2007), 129–138.
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