On a Mixed Sum-Difference Equation of Volterra-Fredholm Type

Authors

  • B. G. Pachpatte 57 Shri Niketan Colony, Near Abhinay Talkies, Aurangabad (Marashtra), India

DOI:

https://doi.org/10.5644/SJM.05.1.05

Keywords:

Sum-difference equation, Volterra-Fredholm type, finite difference inequality, explicit estimate, properties of solutions, uniqueness of solutions, continuous dependence

Abstract

The main objective of this paper is to study some basic properties of solutions of a mixed sum-difference equation of Volterra-Fredholm type. A variant of a certain finite difference inequality with explicit estimate is obtained and used to establish the results.

 

2000 Mathematics Subject Classification. 34K10, 35K10, 35K10

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References

C. Corduneanu, Integral Equations and Applications, Cambridge University Press, 1991.

M. A. Krasnoselskii, Topological methods in the Theory of Nonlinear Integral Equations, Pergamon Press, Oxford, 1964.

M. Kwapisz, Some existence and uniqueness results for boundary value problems for difference equations, Appl. Anal., 37 (1990), 169–182.

V. P. Mikhailov, Partial Differential Equations, Mir Publishers, Moscow, 1978. [5] B. G. Pachpatte, Inequalities for Finite Difference Equations, Marcel Dekker, Inc., New York, 2002.

B. G. Pachpatte, Integral and Finite Difference Inequalities and Applications, NorthHolland Mathematics Studies, Vol. 205, Elsevier Science B.V., Amsterdam, 2006.

B. G. Pachpatte, On mixed Volterra-Fredholm type integral equations, Indian J. Pure Appl. Math., 17 (1986), 488–496.

B. G. Pachpatte, On Volterra-Fredholm integral equation in two variables, Demonstr. Math. XL (2007), 839–850.

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Published

11.06.2024

How to Cite

Pachpatte, B. G. (2024). On a Mixed Sum-Difference Equation of Volterra-Fredholm Type. Sarajevo Journal of Mathematics, 5(1), 55–62. https://doi.org/10.5644/SJM.05.1.05

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