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Title: Existence theorems for a nonlinear second-order distributional differential equation
Author: Liu, Wei
Ye, Guoju
Zhao, Dafang
Torres, Delfim F. M.
Keywords: Distributional differential equation
Measure differential equation
Stochastic differential equation
Regulated function
Kurzweil–Henstock–Stieltjes integral
Leray–Schauder nonlinear alternative
Issue Date: 2018
Publisher: Elsevier
Abstract: In this work, we are concerned with existence of solutions for a nonlinear second-order distributional differential equation, which contains measure differential equations and stochastic differential equations as special cases. The proof is based on the Leray--Schauder nonlinear alternative and Kurzweil--Henstock--Stieltjes integrals. Meanwhile, examples are worked out to demonstrate that the main results are sharp.
Peer review: yes
DOI: 10.1016/j.jksus.2017.04.009
ISSN: 1018-3647
Appears in Collections:SCG - Artigos

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