Representation of solutions to functional and evolution equations and identification problems

Yu. E. Anikonov

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 591-614.

Résumé

In this paper, some problems of representing solutions to operator-functional and evolution equations are studied. Formulas of such representations for use in some identification problems are presented.

Détail

Keywords: functional equations, iterations, identification problems.
Mots-clés : evolution equations

Bibliographie

[1] J. Aczel, Lectures on Functional Equations and Their Applications, Academic Press, New York, 1966 | MR | Zbl

[2] S. S. Cheng, W. Li, Analytic Solutions of Functional Equations, World Scientific Publishing Company, 2008 | MR

[3] Pl. Kannappan, Functional Equations and Inequalities with Applications, Springer, New York, 2009 | MR | Zbl

[4] M. Kuczma, Functional Equations in a Single Variable, Warszawa, 1968 | MR

[5] M. Kuczma, B. Choczewski, R. Ger, Iterative Functional Equations, Cambridge University Press, 1990 | MR | Zbl

[6] G. P. Pelyakh, A. N. Sharkovskii, Introduction to the Theory of Functional Equations, Naukova dumka, Kiev, 1974 | MR

[7] J. Aczel, J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, 1989 | MR | Zbl

[8] Reference Mathematical Library. Functional Analysis, Nauka, M., 1972 | MR

[9] J. Riordan, Introduction to Combinatorial Analysis, Princeton University Press, 1958 | MR

[10] G. A. Korn, T. M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill Book Company, New York, 1968 | MR

[11] W. Song, G. Yang, F. Lei, “On series-like iterative equation with a general boundary restriction”, Fixed Point Theory Appl., 2009 | MR

[12] W. Zhang, “Discussion on the differentiable solutions of iterated equation $\sum\limits_{i=1}^{n}l_{i}f^{i}(x)=F(x)$”, Nonlinear Anal., 15 (1990), 387–398 | DOI | MR | Zbl

[13] L. Li, W. Zhang, “Construction of usc solutions for a multivalued iterative equation of order $n$”, Results in Mathematics, 62 (2012), 203–216 | DOI | MR | Zbl

[14] J. Matkowski, W. Zhang, “On linear dependence of iterates”, Journal of Applied Analysis, 6 (2000), 149–157 | DOI | MR | Zbl

[15] Yu. E. Anikonov, “The identification problem for the functional equation with a parameter”, JIIPP, 20 (2012), 401–409 | MR

[16] E. Egri, J. A. Rus, “First order iterative functional-differential equation with parameter”, Studia Univ., “Babes-Bolyai”, Mathematica, 52 (2007), 67–79 | DOI | MR

[17] S. S. Cheng, “Smooth solutions of iterative functional differential equations”, Dynamical systems and applications Proceedings (Antalya, Turkey, 2004), 228–252

[18] E. A. Gorin, V. Ya. Lin, “Algebraic equations with continuous coefficients and some problems of the algebraic theory of braids”, Matem. Sb., 78 (1969), 579–610. MR0251712 | MR

[19] Yu. E. Anikonov et al., “Inversion of mapping and inverse problems”, Sib. Elektron. Mat. Izv., 9 (2012), 382–432 | MR

[20] A. Yu. Khrennikov, V. M. Shelkovich, Modern $p$-adic analysis and mathematical physics: theory and applications, Fizmatlit, M., 2012

[21] J. Milnor, Dynamics in One Complex Variable, Vieweg, Wiesbaden, 1999 | MR | Zbl

[22] Yu. E. Anikonov, M. V. Neshchadim, “On inverse problems for equations of mathematical physics with parameter”, Sib. Elektron. Mat. Izv., 9 (2012), 45–64 | MR

[23] V. S. Vladimirov, Equations of mathematical physics, Marcel Dekker, Ins. VI, New York, 1971 | MR | Zbl

[24] V. M. Babich, V. S. Buldyrev, Asymptotic methods in short wave diffraction problems, Nauka, M., 1972 | MR

[25] Yu. E. Anikonov, Some methods of studying multidimensional inverse problems for differential equations, Nauka, Novosibirsk, 1978 | MR

[26] S. P. Kurdyumov, E. S. Kurkina, “Thermal structures in a medium with nonlinear thermal conductivity”, New in synergetics: new reality, new problems, and new generation, Nauka, M., 2007 | Zbl