Such thee problems are considered: initial boundary value problem for nonlinear parabolic equations with variable integral delay, boundary value problem for degenerate nonlinear parabolic equations with variable integral delay, Fourier problem for nonlinear parabolic equations with variable integral delay. The conditions of existence and uniqueness of a classical solution of these problems are obtained.

Agaev G. N. On the first boundary value problem for linear degenerate parabolic equations // Izv. AN Azerbaijan SSR, Series of physical and technical sciences and mathematics. – 1976. – 2. – P. 10–16.

Bokalo M., Dmitriv V. The Fourier problem for a multicomponent evolutionary system of equations with integral delay // Bulletin of Lviv University. Series of mechanics and mathematics. – 2002. – 60. – P. 32-49.

Bokalo M.M., Ilnitska O.V. The boundary value problem for nonlinear parabolic equations with delay and degeneration at the initial moment // Ukr. Mat. Journal – 2016. – 68, No. 9. – P. 1155-1168.

Bokalo M., Ilnytska O. Mixed problems for parabolic equations with variable delay // Buk. mat. zhurn. – 2015. – 3, N1. – P. 16-24.

Bugry O.M. On problems with homogeneous boundary conditions for nonlinear equations with degeneration // Ukr. mat. visnyk. – 2008. – 5. – P. 435–469.

Drin S.S., Drin Ya.M. Cauchy problem for the fractal diffusion equation with deviation of the argument // Bukovynskyi mat. zhurn. – 2015. – 3, N2. – P. 23-26.

Elsholts L.E., Norkin S.B. Introduction to the theory of differential equations with an inclined argument - M.: Nauka, 1971.— 296 p.

Ladyzhenskaya O.A., Uraltseva N.N., Solonnikov V.A. Linear and quasi-linear equations of the parabolic type - M.: Nauka, 1967. —736 c.

Myshkis A.D. Linear differential equations with a lagging argument - M.: Nauka, 1972. - 256 c.

Pukalskyi, I. D. The nonlocal Neumann problem for a parabolic equation with degeneracy // Ukr. mate. journal - 1999. - 51, N9. - S. 1232-1243.

Slyusarchuk V.Yu. Absolute stability of dynamic systems with consequences. – R.: UDUVH, 2003. –– 288 p.

Friedman A. Equations in partial derivatives of the parabolic type. - M.: Mir, 1968. - 428 p.

Akimenko V., Anguelov R. Steady states and outbreaks of two-phase nonlinear age-structured model of population dynamics with discrete time delay// J. Biol. Dyn. - 2017. - 11, N1. – P. 75-101, DOI: 10.1080/17513758.2016.1236988

Bainov D., Petrov V. Asymptotic Properties of the Nonoscillatory Solutions of Second-Order Neutral Equations with a Deviating Argument // J. Appl. Math. Anal. Appl. - 1995. - 190. - S. 645–653.

Bokalo M. Dynamical problems without initial conditions for elliptic-parabolic equations in spatial unbounded domains/ M. Bokalo // Electron. J. Differ. Equi. - 2010. - 178. - P. 1-24.

Bokalo M. Linear evolution first-order problems without initial conditions / Bokalo M., Lorenzi A. // Milan J. Math. - 2009. - 77. - P. 437-494.

Burger R., Evje S., Karlsenc K. H. On Strongly Degenerate Convections Diffusion Problems Modeling Sedimentations Consolidation Processes // J. Appl. Math. Anal. Appl. - 2000. - 247. - P. 517-556.

Burton T. A., Haddrock J. R. On the DelayDifferential Equations x′(t)+a(t)f(x(t−r(t))) = 0 and x′′(t) + a(t)f(x(t−r(t))) = 0 // J. Appl. Math. Anal. Appl. - 1976. - 54. - P. 37-48.

Gui-Qiang G. Chen On Degenerate Partial Differential Equations // Oxford Center for Nonlinear PDE. - 2010. - 16. - 38 c.

Dmytriv V.M. On a Fourier problem for coupled evolution system of equations with time delays // Mat. Stud. - 2001. - 16. - P. 141–156.

Dumrongpokaphan T., Lenbury Y., Ouncharoen R., Xu Y. An Intracellular DelayDifferential Equation Model of the HIV Infection and Immune Control // Math. Model. Nat. Phenom. – 2007. – 2. – P. 75–99.

Ivasishen S. D. Parabolic boundary problems without initial conditions // Ukr. Mat. Zh. - 1982. - 34, N5. – P. 547–552.

Feng W., Pao C. V., Lu X. Global Attractors of Reaction-Diffusion Systems Modeling Food Chain Populations with Delays//Commun.PureAppl.Anal. - 2011. - 10. - P. 1463 - 1478.

Lions J.-L. Quelques m´ethodes de r´esolution des probl´emes aux limites non lin´eaires - P.: Dunod Gauthier-Villars, 1969 - 554 p.

Oleinik O. A., Iosifjan G. A. Analog of SaintVenant’s principle and uniqueness of solutions of the boundary problems in unbounded domain for parabolic equations// Usp. Mat. Nauk. - 1976. - 31, N6. - P. 142-166.

Pao C.V. Coupled nonlinear parabolic systems with timedelays//J.Appl.Math.Anal.Appl.–1995.– 196. — P. 237-265.

Pao C.V. Systems of Parabolic Equations with Continuous and Discrete Delays// J. Appl. Math. Anal. Appl. – 1997. – 205. -– P. 157–185.

Tihonov A. N. Uniqueness theorems for the heatequation//Matem.Sbornik.–1935.–2.–P.510516.

Showalter R. E. Monotone operators in Banach space and nonlinear partial differential equations // Amer. Math. Soc., Providence. –1997. – 49. – 278 p.