Abstract
We elaborate on a perturbation technique for examining the existence and uniqueness and delivering the solution in closed form of a composite boundary value problem involving the sum of a linear differential and an integral or loaded operator with nonlocal or integral boundary conditions, assuming that the exact solution for the differential operator with conventional boundary conditions is known. We apply this perturbation method to solve partial integro-differential, or loaded differential, equations with nonlocal, or integral, boundary conditions.
On the occasion of the 100th birthday of Tosio Kato
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Dhage, B.C.: Quadratic perturbations of periodic boundary value problems of second ordinary differential equations. Differ. Equ. Appl. 2(4), 465–486 (2010)
Kato, T.: On the perturbation theory of closed linear operators. J. Math. Soc. Jpn. 4(3–4), 323–337 (1952)
Kato, T.: Perturbation Theory for Linear Operators, Springer, Berlin (1995). https://doi.org/10.1007/978-3-642-66282-9
Kokebaev, B.K., Otelbaev, M., Shynybekov, A.N.: About restrictions and extensions of operators. D.A.N. SSSR 271, 1307–1310 (1983) [Russian]
Oinarov, R.O., Parasidis, I.N.: Correct extensions of operators with finite defect in Banach spaces. Izv. Akad. Kaz. SSR 5, 42–46 (1988) [Russian]
Parasidis, I.N., Providas, E.: Extension operator method for the exact solution of integro-differential equations. In: Pardalos, P.M., Rassias T.M. (eds.) Contributions in Mathematics and Engineering, pp. 473–496. Springer, Berlin (2016). https://doi.org/10.1007/978-3-319-31317-7
Parasidis, I.N., Providas, E.: On the exact solution of nonlinear integro-differential equations: In: Rassias, T.M. (ed.) Applications of Nonlinear Analysis, pp. 591–609. Springer, Cham (2018).https://doi.org/10.1007/978-3-319-89815-5
Sadybekov, M.A., Imanbaev, N.S.: A regular differential operator with perturbed boundary condition. Math. Notes 101(5), 878–887 (2017). https://doi.org/10.1134/S0001434617050133
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Parasidis, I.N., Providas, E. (2019). Exact Solutions to Problems with Perturbed Differential and Boundary Operators. In: Rassias, T.M., Zagrebnov, V.A. (eds) Analysis and Operator Theory . Springer Optimization and Its Applications, vol 146. Springer, Cham. https://doi.org/10.1007/978-3-030-12661-2_14
Download citation
DOI: https://doi.org/10.1007/978-3-030-12661-2_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-12660-5
Online ISBN: 978-3-030-12661-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)