A multipoint problem for partial integro-differential equations
- 25 Downloads
We investigate a multipoint problem for a linear typeless partial differential operator with variable coefficients that is perturbed by a nonlinear integro-differential term. We establish conditions for the unique existence of a solution. We prove metric theorems on lower bounds of small denominators that arise in the course of investigation of the problem of solvability.
KeywordsHyperbolic Equation Small Denominator Unique Existence Unperturbed Problem Multipoint Problem
Unable to display preview. Download preview PDF.
- 2.B. I. Ptashnik, Ill-Posed Boundary-Value Problems for Partial Differential Equations [in Russian], Naukova Dumka, Kiev (1984).Google Scholar
- 3.Yu. M. Berezanskii, Expansion in Eigenfunctions of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965).Google Scholar
- 5.B. I. Ptashnik and V. N. Polishchuk, “Periodic solutions of a system of integro-differential equations of hyperbolic type,” Proceedings of the 8th International Conference on Nonlinear Oscillations (Prague, September 11–15, 1978), Vol. 2, Academia, Prague (1979), pp. 1017–1022.Google Scholar
- 6.B. I. Ptashnik and V. V. Figol’, “A boundary-value problem for a system of integro-differential equations of hyperbolic type,” Mat. Met. Fiz.-Mekh. Polya, Issue 22, 7–11 (1985).Google Scholar
- 8.V. P. Mikhailov, Partial Differential Equations [in Russian], Nauka, Moscow (1983).Google Scholar
- 9.Ya. D. Tamarkin, On Some General Problems in the Theory of Ordinary Differential Equations and Expansion of Arbitrary Functions in Series [in Russian], Petrograd (1917).Google Scholar
- 10.L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1977).Google Scholar
- 13.B. I. Ptashnyk, V. V. Figol’, and P. I. Shtabalyuk, “Solvability, stability, and regularization of the multipoint problem for hyperbolic equations,” Mat. Stud. Pr. L’viv. Mat. Tov., Issue 1, 16–32 (1991).Google Scholar
- 14.B. I. Ptashnyk and P. I. Shtabalyuk, “A multipoint problem for hyperbolic equations in the class of functions almost periodic in space variables,” Mat. Met. Fiz.-Mekh. Polya, Issue 35, 210–215 (1992).Google Scholar
- 15.G. Sansone, Equazioni Differenziali nel Campo Reale [Russian translation], Vol. 1, Inostrannaya Literatura, Moscow (1953).Google Scholar