2018
DOI: 10.1186/s13662-018-1681-0
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Existence and uniqueness of solutions for a class of nonlinear integro-differential equations on unbounded domains in Banach spaces

Abstract: In this paper, the existence and uniqueness of solutions for a class of nonlinear integro-differential equations on unbounded domains in Banach spaces are established under more general conditions by constructing a special Banach space and using cone theory and the Banach contraction mapping principle. The results obtained herein improve and generalize some well-known results.MSC: 47H07; 47H10; 47G20; 34G20

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Cited by 8 publications
(4 citation statements)
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“…Many researchers worked on existence and uniqueness of the solution of IDEs. For more details, one may refer (Guo 2001;Marti 1967;Zhang and Hao 2018) and references therein. Shahmorad (2005) considered the general linear Fredholm-Volterra IDEs, where he used the Tau method to carry out the error estimation of the numerical solution.…”
Section: Introductionmentioning
confidence: 99%
“…Many researchers worked on existence and uniqueness of the solution of IDEs. For more details, one may refer (Guo 2001;Marti 1967;Zhang and Hao 2018) and references therein. Shahmorad (2005) considered the general linear Fredholm-Volterra IDEs, where he used the Tau method to carry out the error estimation of the numerical solution.…”
Section: Introductionmentioning
confidence: 99%
“…We assume in this paper that the equations we intend to solve with our proposed numerical scheme are solvable with unique solutions and omit discussion of ill-posed problems. A number of results on criteria for the existence of solutions are known; see, e.g., [22,34,60] and the references therein. If the variable limit of integration is replaced with a constant value, the integral equations are instead known as Fredholm integral equations [25].…”
Section: Introductionmentioning
confidence: 99%
“…A number of results on criteria for the existence of solutions are known, see e.g. [22,32,57] and the references therein. Interest in efficient algorithms with good convergence properties is high, resulting in a variety of competitive methods for linear, nonlinear and integro-differential Volterra equations.…”
Section: Introductionmentioning
confidence: 99%