There are given definitions and properties of fundamental solution for nonlocal multipoint with respect to time problem for evolution equations with pseudo-differential operators constructed at variable symbols. The solvability of multipoint problem in the W type spaces is installed and the integral image interpretation of solution is given.

Nakhushev A.M. Equations of mathematical biology / A.M. Nakhushev - M.: Higher School, 1995. - 301 p.

Belavyn I.A. Mathematical model of global demographic processes taking into account spatial distribution / I.A. Belavyn, S.P. Kapitsa, S.P. Kurdyumov//Journal of Computational Math. and mat. physicists – 1988. – T.38, N6. - S. 885-902.

Dezin A.A. General questions of the theory of boundary problems / A.A. Dezin - M.: Nauka, 1980. - 208 p.

Romanko V.K. Boundary problems for one class of differential operators / V.K. Romanko // Difference. equations - 1974. - T. 10, N11. - S. 117-131.

Romanko V.K. Nonlocal boundary problems for some systems of equations / V.K. Romanko // Math. notes - 1985. - T. 37, N7. - S. 727-733.

Makarov A.A. Suchestvovaniekorrektnoy two-point boundary value problem in a layer for systems of pseudodifferential equations/A.A. Makarov// Differents.uvravneniya.–1994. - Vol. 30, N1. - P. 144150.

Chesalyn V.I. Problem with nonlocal boundary conditions for abstract hyperbolic equations / V.I. Chesalyn // Difference. equations - 1979. - T.15, N11. - S. 2104-2106.

Ilkiv V.S. Some nonlocal two-point problem for systems of equations with partial derivatives / V.S. Ilkiv, B.I. Poultry // Sib. mate. journal – 2005. – T.46, N1. - S. 119-129.

Lazetic N.L. On classical solutions of mixed boundary problems for one-dimensional parabolic equation of second order / N.L. Lazetic // Publications de Institut Mathematique. - 2000. - Vol. 67. – pp. 5375.

Chabrowski J. On the non-local problems with a functional for parabolic equation / J. Chabrowski // Funkcialaj Ekvacioj. - 1984. - Vol. 27. – pp. 101-123.

Bouziani A. Probleme mixed avec conditions integrales pour une class d'equations paraboliques / A. Bouziani, N.E. Benouar // C.R. Acad. Sci. Paris. Ser. J. - 1995. - Vol. 321. – pp. 1177-1182.

Gelfand I.M. Some questions of the theory of differential equations / I.M. Gelfand, G.E. Shilov. - M.: Fizmatgiz, 1958. - 274 p.

Gurevich B.L. Some spaces of basic and generalized functions and the Cauchy problem for finite-difference schemes / B.L. Gurevich // Dokl. Academy of Sciences of the USSR. – 1954. – T.99, N6. - S. 893-896.

Gelfand I.M. Spaces of basic and generalized functions / I.M. Gelfand, G.E. Shilov. - M.: Fizmatgiz, 1958. - 307 p.

Horodetsky V.V. Cauchy problem for evolutionary equations with differentiation operators of infinite order / V.V. Gorodetsky, O.M. Lenyuk // Bulletin of Kyiv University. Series: Phys.-Math. Sciences. – 2000. – Issue 4. – P. 65-70.

Gorodetsky V.V. Evolutionary pseudodifferential equations in countably normed spaces / V.V. Gorodetsky, O.V. Martynyuk. –Chernivtsi: Tekhnodruk, 2016. – 340 p.