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## Existence and uniqueness of solution to nonlinear second-order distributional differential equations

#### Feng CHEN [1] , Guoju YE [2] , Wei LİU [3] , Dafang ZHAO [4]

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 uniqueness theorems are established by using Schaefer's fixed point theorem and Banach's contraction mapping principle. Examples are given to demonstrate that the results are nontrivial.
Regulated functions, Functions of bounded variation, Distributional differential equation, Schaefer’s fixed point theorem, Banach’s contraction mapping principle
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Primary Language en Mathematics Mathematics Orcid: 0000-0001-6957-3120Author: Feng CHEN (Primary Author)Institution: Hohai UniversityCountry: China Orcid: 0000-0003-4671-049XAuthor: Guoju YE Institution: Hohai UniversityCountry: China Orcid: 0000-0003-4292-0174Author: Wei LİU Institution: Hohai UniversityCountry: China Orcid: 0000-0001-5216-9543Author: Dafang ZHAO Institution: Hubei Normal UniversityCountry: China Publication Date : February 6, 2020
 Bibtex @research article { hujms535238, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {170 - 179}, doi = {10.15672/HJMS.2019.670}, title = {Existence and uniqueness of solution to nonlinear second-order distributional differential equations}, key = {cite}, author = {CHEN, Feng and YE, Guoju and LİU, Wei and ZHAO, Dafang} } APA CHEN, F , YE, G , LİU, W , ZHAO, D . (2020). Existence and uniqueness of solution to nonlinear second-order distributional differential equations. Hacettepe Journal of Mathematics and Statistics , 49 (1) , 170-179 . DOI: 10.15672/HJMS.2019.670 MLA CHEN, F , YE, G , LİU, W , ZHAO, D . "Existence and uniqueness of solution to nonlinear second-order distributional differential equations". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 170-179 Chicago CHEN, F , YE, G , LİU, W , ZHAO, D . "Existence and uniqueness of solution to nonlinear second-order distributional differential equations". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 170-179 RIS TY - JOUR T1 - Existence and uniqueness of solution to nonlinear second-order distributional differential equations AU - Feng CHEN , Guoju YE , Wei LİU , Dafang ZHAO Y1 - 2020 PY - 2020 N1 - doi: 10.15672/HJMS.2019.670 DO - 10.15672/HJMS.2019.670 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 170 EP - 179 VL - 49 IS - 1 SN - 2651-477X-2651-477X M3 - doi: 10.15672/HJMS.2019.670 UR - https://doi.org/10.15672/HJMS.2019.670 Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Existence and uniqueness of solution to nonlinear second-order distributional differential equations %A Feng CHEN , Guoju YE , Wei LİU , Dafang ZHAO %T Existence and uniqueness of solution to nonlinear second-order distributional differential equations %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 1 %R doi: 10.15672/HJMS.2019.670 %U 10.15672/HJMS.2019.670 ISNAD CHEN, Feng , YE, Guoju , LİU, Wei , ZHAO, Dafang . "Existence and uniqueness of solution to nonlinear second-order distributional differential equations". Hacettepe Journal of Mathematics and Statistics 49 / 1 (February 2020): 170-179 . https://doi.org/10.15672/HJMS.2019.670 AMA CHEN F , YE G , LİU W , ZHAO D . Existence and uniqueness of solution to nonlinear second-order distributional differential equations. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 170-179. Vancouver CHEN F , YE G , LİU W , ZHAO D . Existence and uniqueness of solution to nonlinear second-order distributional differential equations. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 179-170.

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