Mixed Functional Differential Equations
Contemporary Mathematics. Fundamental Directions, Functional differential equations, Tome 4 (2003), pp. 5-120.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{CMFD_2003_4_a0,
     author = {A. D. Myshkis},
     title = {Mixed {Functional} {Differential} {Equations}},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {5--120},
     publisher = {mathdoc},
     volume = {4},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2003_4_a0/}
}
TY  - JOUR
AU  - A. D. Myshkis
TI  - Mixed Functional Differential Equations
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2003
SP  - 5
EP  - 120
VL  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2003_4_a0/
LA  - ru
ID  - CMFD_2003_4_a0
ER  - 
%0 Journal Article
%A A. D. Myshkis
%T Mixed Functional Differential Equations
%J Contemporary Mathematics. Fundamental Directions
%D 2003
%P 5-120
%V 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2003_4_a0/
%G ru
%F CMFD_2003_4_a0
A. D. Myshkis. Mixed Functional Differential Equations. Contemporary Mathematics. Fundamental Directions, Functional differential equations, Tome 4 (2003), pp. 5-120. http://geodesic.mathdoc.fr/item/CMFD_2003_4_a0/

[1] Barbashin E. A., Vvedenie v teoriyu ustoichivosti, Nauka 1967, M.

[2] Berezanskii Yu. M., Razlozhenie po sobstvennym funktsiyam samosopryazhennykh operatorov, Naukova Dumka, Kiev, 1965

[3] Berezin I. S., Zhidkov N. P., Metody vychislenii, t. 2, Nauka, M., 1962

[4] Borevich Z. I., Shafarevich I. R., Teoriya chisel, Nauka, M., 1985

[5] Gantmakher F. R., Krein M. G., Ostsillyatsionnye matritsy i yadra, i malye kolebaniya mekhanicheskikh sistem, Gostekhizdat, M.–L., 1950

[6] Gradshtein I. S., Ryzhik I. M., Tablitsa integralov, summ, ryadov i proizvedenii, Fizmatgiz, M., 1962

[7] Daletskii Yu. L., Krein M. G., Ustoichivost reshenii differentsialnykh uravnenii v banakhovom prostranstve, Nauka, M., 1970

[8] Danford N., Shvarts Dzh., Lineinye operatory, t. 1, IL, M., 1962

[9] Zhukovskii N. E., “Rabota (usilie) russkogo skvoznogo i amerikanskogo neskvoznogo tyagovykh priborov pri troganii poezda s mesta i v nachale ego dvizheniya”, Poln. sobr. soch., t. 8, ONTI, M.–L., 1937, 221–255

[10] Ivanova E. P., Kamenskii G. A., Variatsionnye i kraevye zadachi dlya differentsialno-raznostnykh uravnenii, MAI, M., 1993

[11] Ivanova E. P., Kamenskii G. A., Nachalnye zadachi dlya differentsialno-raznostnykh uravnenii, MAI, M., 1995

[12] Kauling T. D., Chepmen S., Matematicheskaya teoriya neodnorodnykh gazov, IL, M., 1960

[13] Keiz K., Tsvaifel P. F., Lineinaya teoriya perenosa, Mir, M., 1972

[14] Kurchanov P. F., Myshkis A. D., Filimonov A. M., “Kolebaniya zheleznodorozhnogo sostava i teorema Kronekera”, Prikl. mat. i mekh., 55:6 (1991), 989–995 | MR | Zbl

[15] Lure A. I., Operatsionnoe ischislenie i ego prilozheniya k zadacham mekhaniki, Gostekhizdat, M.–L., 1960

[16] Lyusternik L. A., Sobolev V. I., Elementy funktsionalnogo analiza, Nauka, M., 1965

[17] Marchuk G. I., Lebedev V. I., Chislennye metody v teorii perenosa neitronov, Atomizdat, M., 1981

[18] Myshkis A. D., Lineinye differentsialnye uravneniya s zapazdyvayuschim argumentom, izdanie vtoroe, Nauka, M., 1972

[19] Myshkis A. D., “Nachalnaya zadacha dlya smeshannykh funktsilnalno-differentsialnykh uravnenii”, Avtomatika i telemekhanika, 1999, no. 3, 170–180

[20] Myshkis A. D., “$L^2$-ustoichivost lineinykh prostranstvenno-odnorodnykh smeshannykh funktsionalno-differentsialnykh uravnenii”, Diff. ur-ya, 36:1 (2000), 71–75 | MR

[21] Myshkis A. D., “Ustoichivost lineinykh smeshannykh funktsionalno-differentsialnykh uravnenii s soizmerimymi otkloneniyami prostranstvennogo argumenta”, Diff. ur-ya, 38:10 (2002), 1331–1337 | MR | Zbl

[22] Pinni E., Obyknovennye differentsialno-raznostnye uravneniya, IL, M., 1960

[23] Pontryagin L. S., Nepreryvnye gruppy, izdanie trete, Nauka, M., 1973

[24] Khalmosh P., Teoriya mery, IL, M., 1953

[25] Appel J., Diallo O. W., “Problemes aux limites pour des equations integro-differentielles de type Barbachine”, Z. Anal. Anwendungen, 14:1 (1995), 95–104 | MR | Zbl

[26] Bernoulli J., “Dechordis vibrantibls”, Commentarii Academiae Scientiarum Imperialis Petropolitanae, 3 (1728), 13–28

[27] Burkhardt H., “Entwicklungen nach oscillirenden Funktionen und Integration der Differentialgleichungen der mathematischen Physik”, Jahresber. Deutsch. Math.-Verein, 10 (1908), 1–1804

[28] Ceppitelli R., Kamont Z., “Extremal solutions for semilinear differential–functional systems in two independent variables”, Atti Sem. Mat. Fis. Univ. Modena, 42:2 (1994), 329–341 | MR | Zbl

[29] Chur-jen Chen, “On a generalized integro-differential equation of Barbashin type”, Z. Anal. Anwendungen, 14:4 (1995), 899–912 | MR | Zbl

[30] Dlotko T., “Stability of the Chandrasekhar—Muench equation”, Zesn. Nauk. U. I. Acta Math, 1991, no. 28, 85–92 | MR | Zbl

[31] Elderskin R. H., “Nonlinear, globally age-dependent population models; some basic theory”, J. Math. Appl., 108:2 (1985), 546–562 | MR

[32] Ermolova E. A., “Lyapunov–Bohl–Exponent und Greensche Funktion fuer eine Klasse von Integro-Differentialgleichungen”, Z. Anal. Anwendungen, 14:4 (1995), 881–898 | MR | Zbl

[33] Filimonov A. M., Kurchanov P. F., Myshkis A. D., “Some unexpected results in the classical problem of vibration of the string with $n$ beads when $n$ is large”, C. R. Acad. Sci. Paris Sér. I Math., 313 (1991), 961–965 | MR | Zbl

[34] Filimonov A. M., Myshkis A. D., “On approximation of differential operator with differential one by investigation of oscillations of 1-dimensional discrete systems”, Advances in Difference Equations, Proc. of the Second Intern. Conf. on Difference Equations (Vesprém, Hungary, August 7–11 1995), 197–204 | MR | Zbl

[35] Filimonov A. M., Myshkis A. D., “Asymptotic estimate of solution of one mixed difference-differential equation of oscillations theory”, J. Differ. Equations Appl., 4 (1998), 13–16 | DOI | MR | Zbl

[36] Gopalsamy K., “Age-specific coexistence in two-species competition”, Math. Biosci, 61:1 (1982) | DOI | MR | Zbl

[37] Grant Ch. P., Van Vleck E. S., “Slowly-migrating transition layers for the discrete Allen—Cahn and Cahn–Hilliard equations”, Nonlinearity, 8:5 (1995), 861–876 | DOI | MR | Zbl

[38] Ivanova E. P., Kamenskii G. A., On initial value problems for a differential-difference equation, Techn. Report No 63, Univ. of Rhode Island, USA, 1991

[39] Kamenskii G. A., “Boundary value problems for differential-difference equations arising from variational problems”, Nonlinear Anal., Theory Methods Appl., 18:8 (1992), 801–813 | DOI | MR

[40] Kamenskii G. A., Myshkis A. D., “On the mixed type functional differential equations”, Nonlinear Anal., Theory Methods Appl., 30:5 (1997), 2577–2584 | DOI | MR | Zbl

[41] Kamenskii G. A., Myshkis A. D., “Periodic solutions of linear inhomogeneous mixed functional differential equations”, Funct. Differ. Equ., 4:1–2 (1997), 81–90 | MR | Zbl

[42] Kamenskii G. A., Myshkis A. D., “Mixed functional differential equations”, Nonlinear Anal., Theory Methods Appl., 34:2 (1998), 283–297 | DOI | MR | Zbl

[43] Kolmanovskii V., Myshkis A., Introduction to the Theory and Applications of Functional Differential Equations, Kluwer Acad. Press, Dortmund–Boston–London, 1999 | MR | Zbl

[44] Kwan C. M., “Some new results in population control”, Proc. 33rd IEEE Conf. Decis. and Contr., vol. 4 (Lake Buena Vista, Fla, Dec. 14–16 — 1994), 4110–4111

[45] Lagrange G. L., Mechanique Analitique Paris, 1788

[46] Lee N., Sibuja Y., “A note on partial differential-difference equation”, J. Difference Equ. Appl., 7 (2001), 13–20 | DOI | MR | Zbl

[47] Leszczynski H., “Convergence result for unbounded solutions of first order non-linear differential-functional equations”, Ann. Pol. Math., 64:1 (1996), 1–16 | MR | Zbl

[48] Milner F. A., “Age structured populations with history dependent mortality and natality”, Calcolo, 30:1 (1993), 29–39 | DOI | MR | Zbl

[49] Myshkis A. D., “On the solvability of the initial-boundary problem for mixed functional-differential equation of retarded type”, Funct. Differ. Equ., 7:3–4 (2000) | MR | Zbl

[50] Myshkis A. D., “Stability of linear spatially uniform mixed functional-difference equations”, J. Difference Equ. Appl., 7 (2001), 941–949 | DOI | MR | Zbl

[51] Myshkis A. D., “Mixed functional differential equations with continuous and piecewise continuous solutions”, Funct. Differ. Equ., 9:1–2 (2002), 221–226 | MR | Zbl

[52] Perron O., Die Lehre von dan Kettenbruehen, Bd. 1–2, Stuttg., 1954–1957

[53] Rothe E. H., “Zweidimensionale parabolische Randwertaufgaben als Grenzfall eindimensionaler Randwertaufgaben”, Math. Ann., 102:4/5 (1929)

[54] Stewart I. W., Dubovskii P. B., “Approach to equilibrium for the coagulation-fragmentation equation via a Lyapunov functional”, Math. Appl. Sci., 19:3 (1996), 171–185 | 3.0.CO;2-7 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[55] Tarallo M., Terracini S., “On the existence of periodic and solitary traveling waves in some non linear lattices”, Dyn. Syst. Appl., 4:3 (1995), 429–458 | MR | Zbl

[56] Truesdell C., An essay towards a unified theory of special functions, Princeton Univ. Press, Princeton, 1948 | MR | Zbl