Existence and uniqueness of solution to nonlinearsecond-order distributional differential equations

Objective & Hypothesis:The aim of this paper is to obtain solutions in terms of regulated functions to second-order distributional differential equations for Dirichlet problem.

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Key Findings & Data:Existence and uniquenesstheorems are established by using Schaefer’s fixed point theorem and Banach’s contractionmapping principle.

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Conclusion & Impact:Examples are given to demonstrate that the results are nontrivial.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:Domain Parameters

Abstract

The aim of this paper is to obtain solutions in terms of regulated functions to second-order distributional differential equations for Dirichlet problem. Existence and uniquenesstheorems are established by using Schaefer’s fixed point theorem and Banach’s contractionmapping principle. Examples are given to demonstrate that the results are nontrivial.

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Cite This Article

CHEN, F., YE, G., LİU, W., ZHAO, D. (2022). Existence and uniqueness of solution to nonlinearsecond-order distributional differential equations. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 1, 170–179. https://ajindex.com/articles/529676

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References (1)

J. Appell, J. Banaś and N. Merentes,Bounded variation and around, in: De GruyterSeries in Nonlinear Analysis and Applications,17, De Gruyter, Berlin, 2014. [2]P.C. Das and R.R. Sharma,Existence and stability of measure differential equations,Czechoslovak Math. J.22(97), 145–158, 1972. [3]M. Federson, R. Grau, J.G. Mesquita and E. Toon,Boundedness of solutions ofmeasure differential equations and dynamic equations on time scales, J. DifferentialEquations,263(1), 26–56, 2017. [4]D. Fraňková,Regulated functions, Math. Bohem.116(1), 20–59, 1991. [5]W.A. Kirk and B. Sims,Handbook of Metric Fixed Point Theory, Kluwer AcademicPublishers, Dordrecht, 2001. [6]P.Y. Lee,Lanzhou lectures on Henstock integration, World Scientific, Singapore, 1989. [7]S. Leela,Stability of measure differential equations, Pacific J. Math.55, 489–498,1974. [8]G.A. Monteiro and A. Slavík,Linear measure functional differential equations withinfinite delay, Math. Nachr.287(11-12), 1363–1382, 2014. [9]G.A. Monteiro and A. Slavík,Extremal solutions of measure differential equations, J.Math. Anal. Appl.444(1), 568–597, 2016. [10]A. Slavík,Measure functional differential equations with infinite delay, NonlinearAnal.79, 140–155, 2013. [11]A. Slavík,Well-posedness results for abstract generalized differential equations andmeasure functional differential equations, J. Differential Equations,259(2), 666–707,2015. [12]M. Tvrdý,Differential and integral equations in the space of regulated functions, Mem.Differential Equations Math. Phys.25, 1–104, 2002. [13]G. Ye and W. Liu,The distributional Henstock-Kurzweil integral and applications,Monatsh. Math.181(4), 975–989, 2016. [14]J.H. Yoon, G.S. Eun and Y.C. Lee,On Henstock-Stieltjes integral, Kangweon KyungkiJ. Math.6, 87–96, 1998. [15]E. Zeidler,Nonlinear Functional Analysis and its Applications, I - Fixed-Point The-orems, Springer-Verlag, New York, 1986.