The review of works of the author and his students concerning research in cylindrical domains of correct solvability of problems with local multipoint conditions on the time variable for the evolutionary partial differential equations and systems (linear and weakly nonlinear), which, in general, are conditionally well-posed by Hadamard, and their solvability related to the problem of small denominators is given.

[1] Picone M. Sui valori eccezionali di un parametro do cui dipende un equazione differentiale lineare ordinaria del secondo ordine. – Pisa, 1909. – 176 p.

[2] Tamarkin Y.D. On some general problems of the theory of ordinary differential equations and on the decomposition of arbitrary functions into series.- Petrograd, 1917. - 308+XIV p.

[3] Vallée-Poussin de la Ch.J. Sur l’ équation différentielle linéaire du second orde. Determination d’une intégrale par deux valeurx assignées. Extension aux eqautions d’orde n//J. math. pura et appl. – 1929. – 9 , № 8. – P.125–144.

[4] Ptashnik B.Y. Vallee-Poussin type problem for hyperbolic equations with constant coefficients - Doklad. AN URSR - 1966. - № 10. - P. 1254-1257.

[5] Ptashnik B.I. Non-correct boundary value problems for differential equations with partial derivatives. - Kiev: Nauk. dumka, 1984. - 264 p.

[6] Grebennikov E.A., Ryabov Y.A. Resonances and small denominators in celestial mechanics. - Moscow:Nauka, 1978. - 128 p.

[7] Kolmogorov A.N. On dynamical systems with an integral invariant on the torus// Dokl. ANSSR. - 1953. - 93, № 5. - P. 763-766.

[8] Arnold V.I. Small denominators and problems of stability of motion in classical and celestial mechanics// Uspekhi mat. nauki. - 1963. -18, v.6. - P. 91-192.

[9] Moser, Y. Fast convergent method of iterations and nonlinear differential equations  // Ibidem. - 1968. -P.179-238.

[10] Baker J.(jr). Graves-Morris P. Approximations of Padé. - Moscow: Mir, 1986. - 502 p.

[11] Groshev A.V. Theorem on the system of linear forms// Dokl. of the USSR Academy of Sciences. - 1938.-19, № 3. - P. 151-152.

[12] Sprinjuk V.G. Metric theory of Diophantine approximations. - Moscow: Nauka, 1977. -143 p.

[13] Bernik V., Beresnevich V. On a metrical theorem of W. Scmidt// Acta Arithm. – 1996. – 75 , № 3. – P. 219–233.

[14] Bernik V.I., Ptashnik B.I., Saliga B.O. An analogue of the multipoint problem for the hyperbolic equation with constant coefficients/Differential Equations.- 1977.-13, № 4.- P.637-645.

[15] Ilkiv V.S., Ptashnik B.I. Problem with nonlocal boundary conditions for systems of partial differential equations with constant coefficients// Differential Equations. - 1984. -20, № 6. - P. 1012-1023.

[16] Ptashnyk B.Y., Simotiuk M.M. Multipoint problem for non-isotropic partial differential equations with constant coefficients // Ukrainian Mathematical Journal - 2003.- 55, № 2.- P.241-254.

[17] Khinchin A.Ya.Chain fractions. - Moscow: Nauka, 1978. - 112 p.

[18] Khintschine A. Zur metrischen Theorie der diophantischen Approximationen// Math. Zeitschrift. – 1926. – 24 . – S. 706–714.

[19] Jarnik V. Diophantische Approximation und Hausdorffsches Mass// Mat. Sb. – 1929. – 36 , № 3/4. – S. 371–382.

[20] Besicovitch A.S. Sets of fractional dimensions on rational approximations to real numbers// J. London Math. Soc. – 1934. – 9 . – P. 126–131.

[21] Hausdorff F. Dimension undäusseres Mass// Math. Ann. – 1918. – 79 . – S. 157–179.

[22] Billingsley P. Ergodic Theory and Information. - Moscow: Mir, 1969. - 238 p.

[23] Arnold V.I. Small denominators. 1. On the mapping of a circle onto itself // Izv. of the USSR Academy of Sciences, Ser. mat. - 1961. -25, № 1. - P. 21-86.

[24] Ptashnik B.I. The problem of the Vallée Poussin type and some boundary value problems for linear hyperbolic equations. Cand. of Phys.-Math. sciences. - Lvov, 1967. - 11 p.

[25] Klyus I.S., Ptashnyk B.Y. Three-point problem for the wave equation// Bulletin of Lviv University. Ser. Mech.–Mat. – 1996. – Issue 45. – P. 78–86.

[26] Klyus I.S. Multipoint problems for hyperbolic equations and equations not solved with respect to the higher derivative// Abstract of the dissertation ... candidate of physical and mathematical sciences – Lviv, 2003. – 18 p.

[27] Bernik V.I., Beresnevich V.V., Vasylyshyn P.B., Ptashnyk B.Y. Multipoint problem with multiple nodes for linear hyperbolic equations// Ukr. mat. zhurn.– 1999.– 51 , № 10.– P. 1311–1316.

[28] Vasylyshyn P.B. Multipoint problems for differential equations and systems of equations with partial derivatives// Author's abstract of the dissertation ... candidate of physical and mathematical sciences. – Chernivtsi, 2001. – 19 p.

[29] Bernik V.I., Vasylyshyn P.B., Ptashnyk B.Yu. Multipoint problem for weakly nonlinear hyperbolic equations// Bulletin of the National University of Lviv Polytechnic. № 411. Applied Mathematics. – Lviv, 2000. – P. 11–17.

[30] Ptashnyk B.Y. Analogue of the $n$-point problem for a linear hyperbolic equation// Ukr. Mat. Journal – 1971. – 23, № 4. – P. 472–478.

[31] Ptashnyk B.Y., Figol V.V., Shtabaliuk P.I. Solvability, stability and regularization of a multipoint problem for hyperbolic equations// Math. Studio. Proceedings of the Lviv Math. Society. – 1991. – Issue 1. – P. 16–32.

[32] Salyga B.O. A multipoint problem for differential equations with partial derivatives// Autoref. thesis ... candidate phys.-math. of science – Donetsk, 1986. – 14 p.

[33] Shtablyuk P.I. Almost periodic solutions of differential equations of hyperbolic and compound types// Autoref. thesis ... candidate of physics and mathematics of science - Minsk, 1984. - 17 p.

[34] Ptashnik B.Y., Shtabaliuk P.I. Multipoint problem for hyperbolic equations in the class of functions almost periodic in spatial variables// Mat. methods and physical-mechanical fields. – 1992. – Issue 35. – P. 210–215.

[35] Ptashnik B.Y. Analogue of the $n$-point problem for systems of hyperbolic equations with constant coefficients// Supplement to the Academy of Sciences of the Ukrainian SSR. Ser. A. – 1974. – № 8. – P. 709–712.

[36] Ptashnyk B.I. An analogue of the multipoint problem for a hyperbolic operator decomposing into wave multiples// Mat. physics – 1974. – Issue 16. - P. 167–174.

[37] Antipko I.Y., Perelman M.A. On the uniqueness classes of the solution of a nonlocal multipoint boundary value problem in an infinite layer // Theory of functions, funktsion. analysis and their applications. -1972. – Issue 16. - P. 98–109

[38] Borok V.M., Perelman M.A. On the uniqueness classes of the solution of a multipoint boundary value problem in an infinite layer// Izv. universities Mathematics. – 1973. – № 8. – P. 29–34

[39] Nicoletti O. Sulle condisioni iniziali che determiniano gli integrali della equazioni differenziali ordinarie// Atti della R.Acc.Sc.Torino. – 1897–1898. – 33 . – P. 746–759.

[40] Kalenyuk P.I., Nytrebych Z.M. Generalized scheme of separation of variables. Differential-symbolic method. – Lviv: Publishing house of the National University "Lviv Polytechnic", 2002. – 292 p.

[41] Kalenyuk P.I., Nytrebych Z.M., Pleshevsky Ya.M. Boundary value problem with local multipoint conditions for a homogeneous polylinear system of equations with partial derivatives// Mat. methods and phys.–mech. fields. – 2000. – 43, № 2 – P.90–95.

[42] Kalenyuk P.I., Nytrebych Z.M., Pleshevsky Ya.M. Multipoint problem for a non-homogeneous polylinear system of partial differential equations// Bulletin of Lviv Polytechnic University. Ser. Mech.–Mat. – 2000. – Issue 58. – P.144–152.

[43] Klyus I.S., Nytrebych Z.M. Multipoint problem for a partial differential equation that decomposes into a product of linear factors with respect to differentiation// Bulletin of the National University "Lviv Polytechnic". № 407. Applied Mathematics. –Lviv, 2000. – P. 220–226.

[44] Ptashnyk B.Yu. Vallee–Poussin type problem for linear hyperbolic equations with variable coefficients// Supplement to the Academy of Sciences of the Ukrainian SSR.– 1967.– № 2.– P. 127–130.

[45] Salyga, B.O. An analogue of the multipoint problem for a non-strict hyperbolic operator with coefficients varying over $t$// Mat. physical and mechanical methods fields – 1979. – Issue 9. - P. 9–14.

[46] Ptashnyk B.I., Salyga B.O. An analogue of the multipoint problem for differential equations with partial derivatives with variable coefficients//Ukr. mate. journal – 1983. –35, № 6. – S. 728–734.

[47] Vasylyshyn P.B., Klyus I.S., Ptashnyk B.Y. Multipoint problem for hyperbolic equations with variable coefficients// Ukr.mat. zhurn. – 1996. – 48, № 11. – P. 1468–1476.

[48] Vasylyshyn P.B., Ptashnyk B.Y. Multipoint problem for integro-differential equations with partial derivatives// Ukr.mat. zhurn. – 1998. – 50, № 9. – P. 1155–1168.

[49] Silyuga L.P. Multipoint problem for linear parabolic and atypical differential equations and systems of equations with partial derivatives// Author's thesis.... Candidate of Physical and Mathematical Sciences – Lviv, 1996.– 24 p.

[50] Silyuga L.P. Multipoint problem for parabolic equations with constant coefficients// Math. Methods and Physical and Mechanical Fields.– 2000.– 43, № 4.– P.42–48.

[51] Ptashnyk B.Yu., Tymkiv I.R. Multipoint problem for high-order parabolic equations in a parallelepiped// Nonlinear oscillations. – 2009. – 12, № 3. – P. 336–346.

[52] Ptashnyk B.Y., Tymkiv I.R. Multipoint problem for a parabolic equation with variable coefficients in a cylindrical domain// Math. methods and phys.–mechanics fields.

[53] Symotyuk M.M. Multipoint problems for linear differential and pseudodifferential equations with partial derivatives// Author's abstract of the dissertation ... candidate of physical and mathematical sciences. – Lviv, 2005. – 17 p.

[54] Komarnytska L.I. Boundary-value problems for differential equations and systems with partial derivatives, not solved with respect to the highest derivative in time// Author's abstract of the dissertation ... candidate of physical and mathematical sciences. – Lviv, 1995. – 24 p.

[55] lkiv V.S., Polishchuk V.N., Ptashnyk B.I., Salyga B.O. Nonlocal multipoint problem for pseudodifferential operators with analytic symbols// Ukr. mate. journal – 1986. –38, № 5. – P. 582–587.

[56] Dubinsky Yu.A. Algebra of pseudodifferential operators with analytical symbols and applications to mathematical physics//Uspekhimat. of science – 1982. –37, issue 5(227). – P. 97–159.

[57] Ptashnyk B.Y., Ilkiv V.S., Kmit I.Ya., Polishchuk V.M. Nonlocal boundary value problems for partial differential equations. – Kyiv: Nauk. Dumka, 2002. – 415 p.

[58] Ilkiv V.S. Nonlocal boundary value problems for partial differential equations and differential operator equations// Author’s abstract of the dissertation ... doctor of physical and mathematical sciences. – Kyiv, 2005. – 32 p.

[59] Ptashnyk B.Y., Galun K.S. Multipoint problem for factorized hyperbolic-parabolic operators // Supplement to the NAS of Ukraine. – 2009. – № 11. – P. 33–38.

[60] Galun K.S., Ptashnyk B.Yu. Multipoint problems for typeless evolutionary equations with constant coefficients // Mater. 13th International Conference named after Academician M. Kravchuk. T. 1. – Kyiv, 2010. – P. 99.