Araştırma Makalesi
BibTex RIS Kaynak Göster

Existence of solutions for impulsive boundary value problems on infinite intervals

Yıl 2023, Cilt: 72 Sayı: 3, 721 - 736, 30.09.2023
https://doi.org/10.31801/cfsuasmas.1186785

Öz

The paper deals with the existence of solutions for a general class of second-order nonlinear impulsive boundary value problems defined on an infinite interval. The main innovative aspects of the study are that the results are obtained under relatively mild conditions and the use of principal and nonprincipal solutions that were obtained in a very recent study. Additional results about the existence of bounded solutions are also provided, and theoretical results are supported by an illustrative example.

Kaynakça

  • Agarwal, R. P., O’Regan, D., Infinite Interval Problems for Differential, Difference and Integral Equations, Netherlands: Kluwer Academic Publisher, 2001. https://doi.org/10.1007/978-94-010-0718-4.
  • Akgöl, S. D., Zafer, A., Boundary value problems on half-line for second-order nonlinear impulsive differential equations, Math. Meth. Appl. Sci., 41 (2018), 5459–5465. https://doi.org/10.1002/mma.5089
  • Akgöl, S.D., Zafer, A., A fixed point approach to singular impulsive boundary value problems, AIP Conference Proceedings, 1863 (2017), 140003. https://doi.org/10.1063/1.4992310
  • Akgöl, S. D., Zafer, A., Prescribed asymptotic behavior of second-order impulsive differential equations via principal and nonprincipal solutions, J. Math. Anal. Appl., 503(2) (2021), 125311. https://doi.org/10.1016/j.jmaa.2021.125311
  • Akgöl, S. D., Zafer, A., Leighton and Wong type oscillation theorems for impulsive differential equations, Appl. Math. Lett., 121 (2021), 107513. https://doi.org/10.1016/j.aml.2021.107513
  • Bainov, D., Simeonov, P., Impulsive Differential Equations: Asymptotic Properties of the Solutions, World Scientific, Singapore, 1995. https://doi.org/10.1142/2413
  • Ertem, T., Zafer, A., Existence of solutions for a class of nonlinear boundary value problems on half-line, Bound. Value Probl., 43 (2012). https://doi.org/10.1186/1687-2770-2012-43
  • Hanche-Olsen, H., Holden, H., The Kolmogorov-Riesz compactness theorem, Expo. Math., 28 (2010), 385-394. https://doi.org/10.1016/j.exmath.2010.03.001
  • Iswarya, M., Raja, R., Rajchakit, G., Cao, J., Alzabut, J., Huang, C., A perspective on graph theory-based stability analysis of impulsive stochastic recurrent neural networks with timevarying delays, Adv. Differ. Equ., 502 (2019). https://doi.org/10.1186/s13662-019-2443-3
  • Karaca, İ. Y., Aksoy, S., Existence of positive solutions for second-order impulsive differential equations with integral boundary conditions on the real line, Filomat, 35(12) (2021), 4197-4208. https://doi.org/10.2298/FIL2112197K
  • Kayar, Z., An existence and uniqueness result for linear fractional impulsive boundary value problems as an application of Lyapunov type inequality, Hacet. J. Math. Stat., 47(2) (2018), 287-297. Doi:10.15672/HJMS.2017.463
  • Li, Z., Shu, X. B., Xu, F., The existence of upper and lower solutions to second-order random impulsive differential equation with boundary value problem, AIMS Mathematics, 5(6) (2020), 6189-6210. https://doi.org/10.3934/math.2020398
  • Özbekler, A., Zafer, A., Principal and nonprincipal solutions of impulsive differential equations with applications, Appl. Math. Comput., 216 (2010), 1158-1168. https://doi.org/10.1016/j.amc.2010.02.008
  • Riesz, M., Sur les ensembles compacts de fonctions sommables, Acta Szeged Sect. Math., 6 (1933), 136-142.
  • Royden, H. L., Real Analysis, 2nd. ed. Macmillan, 1968.
  • Samoilenko, A. M., Perestyuk, N. A., Impulsive Differential Equations, World Scientific, 1995.
  • Vinodkumar, A., Senthilkumar, T., Hariharan, S., Alzabut, J., Exponential stabilization of fixed and random time impulsive delay differential system with applications, Math. Biosci. Eng., 18(3) (2021), 2384-2400. https://doi.org/10.3934/mbe.2021121
  • Zada, A., Alam, L., Kumam, P., Kumam, W., Ali, G., Alzabut, J., Controllability of impulsive non–linear delay dynamic systems on time scale, IEEE Access, 8 (2020), 93830-93839. https://doi.org/10.1109/ACCESS.2020.2995328.
Yıl 2023, Cilt: 72 Sayı: 3, 721 - 736, 30.09.2023
https://doi.org/10.31801/cfsuasmas.1186785

Öz

Kaynakça

  • Agarwal, R. P., O’Regan, D., Infinite Interval Problems for Differential, Difference and Integral Equations, Netherlands: Kluwer Academic Publisher, 2001. https://doi.org/10.1007/978-94-010-0718-4.
  • Akgöl, S. D., Zafer, A., Boundary value problems on half-line for second-order nonlinear impulsive differential equations, Math. Meth. Appl. Sci., 41 (2018), 5459–5465. https://doi.org/10.1002/mma.5089
  • Akgöl, S.D., Zafer, A., A fixed point approach to singular impulsive boundary value problems, AIP Conference Proceedings, 1863 (2017), 140003. https://doi.org/10.1063/1.4992310
  • Akgöl, S. D., Zafer, A., Prescribed asymptotic behavior of second-order impulsive differential equations via principal and nonprincipal solutions, J. Math. Anal. Appl., 503(2) (2021), 125311. https://doi.org/10.1016/j.jmaa.2021.125311
  • Akgöl, S. D., Zafer, A., Leighton and Wong type oscillation theorems for impulsive differential equations, Appl. Math. Lett., 121 (2021), 107513. https://doi.org/10.1016/j.aml.2021.107513
  • Bainov, D., Simeonov, P., Impulsive Differential Equations: Asymptotic Properties of the Solutions, World Scientific, Singapore, 1995. https://doi.org/10.1142/2413
  • Ertem, T., Zafer, A., Existence of solutions for a class of nonlinear boundary value problems on half-line, Bound. Value Probl., 43 (2012). https://doi.org/10.1186/1687-2770-2012-43
  • Hanche-Olsen, H., Holden, H., The Kolmogorov-Riesz compactness theorem, Expo. Math., 28 (2010), 385-394. https://doi.org/10.1016/j.exmath.2010.03.001
  • Iswarya, M., Raja, R., Rajchakit, G., Cao, J., Alzabut, J., Huang, C., A perspective on graph theory-based stability analysis of impulsive stochastic recurrent neural networks with timevarying delays, Adv. Differ. Equ., 502 (2019). https://doi.org/10.1186/s13662-019-2443-3
  • Karaca, İ. Y., Aksoy, S., Existence of positive solutions for second-order impulsive differential equations with integral boundary conditions on the real line, Filomat, 35(12) (2021), 4197-4208. https://doi.org/10.2298/FIL2112197K
  • Kayar, Z., An existence and uniqueness result for linear fractional impulsive boundary value problems as an application of Lyapunov type inequality, Hacet. J. Math. Stat., 47(2) (2018), 287-297. Doi:10.15672/HJMS.2017.463
  • Li, Z., Shu, X. B., Xu, F., The existence of upper and lower solutions to second-order random impulsive differential equation with boundary value problem, AIMS Mathematics, 5(6) (2020), 6189-6210. https://doi.org/10.3934/math.2020398
  • Özbekler, A., Zafer, A., Principal and nonprincipal solutions of impulsive differential equations with applications, Appl. Math. Comput., 216 (2010), 1158-1168. https://doi.org/10.1016/j.amc.2010.02.008
  • Riesz, M., Sur les ensembles compacts de fonctions sommables, Acta Szeged Sect. Math., 6 (1933), 136-142.
  • Royden, H. L., Real Analysis, 2nd. ed. Macmillan, 1968.
  • Samoilenko, A. M., Perestyuk, N. A., Impulsive Differential Equations, World Scientific, 1995.
  • Vinodkumar, A., Senthilkumar, T., Hariharan, S., Alzabut, J., Exponential stabilization of fixed and random time impulsive delay differential system with applications, Math. Biosci. Eng., 18(3) (2021), 2384-2400. https://doi.org/10.3934/mbe.2021121
  • Zada, A., Alam, L., Kumam, P., Kumam, W., Ali, G., Alzabut, J., Controllability of impulsive non–linear delay dynamic systems on time scale, IEEE Access, 8 (2020), 93830-93839. https://doi.org/10.1109/ACCESS.2020.2995328.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik
Bölüm Research Article
Yazarlar

Sibel Doğru Akgöl 0000-0003-3513-1046

Yayımlanma Tarihi 30 Eylül 2023
Gönderilme Tarihi 10 Ekim 2022
Kabul Tarihi 21 Mart 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 72 Sayı: 3

Kaynak Göster

APA Doğru Akgöl, S. (2023). Existence of solutions for impulsive boundary value problems on infinite intervals. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(3), 721-736. https://doi.org/10.31801/cfsuasmas.1186785
AMA Doğru Akgöl S. Existence of solutions for impulsive boundary value problems on infinite intervals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Eylül 2023;72(3):721-736. doi:10.31801/cfsuasmas.1186785
Chicago Doğru Akgöl, Sibel. “Existence of Solutions for Impulsive Boundary Value Problems on Infinite Intervals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, sy. 3 (Eylül 2023): 721-36. https://doi.org/10.31801/cfsuasmas.1186785.
EndNote Doğru Akgöl S (01 Eylül 2023) Existence of solutions for impulsive boundary value problems on infinite intervals. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 3 721–736.
IEEE S. Doğru Akgöl, “Existence of solutions for impulsive boundary value problems on infinite intervals”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 72, sy. 3, ss. 721–736, 2023, doi: 10.31801/cfsuasmas.1186785.
ISNAD Doğru Akgöl, Sibel. “Existence of Solutions for Impulsive Boundary Value Problems on Infinite Intervals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/3 (Eylül 2023), 721-736. https://doi.org/10.31801/cfsuasmas.1186785.
JAMA Doğru Akgöl S. Existence of solutions for impulsive boundary value problems on infinite intervals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:721–736.
MLA Doğru Akgöl, Sibel. “Existence of Solutions for Impulsive Boundary Value Problems on Infinite Intervals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 72, sy. 3, 2023, ss. 721-36, doi:10.31801/cfsuasmas.1186785.
Vancouver Doğru Akgöl S. Existence of solutions for impulsive boundary value problems on infinite intervals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(3):721-36.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.