Về khả năng giải quyết các phương trình vi phân hàm phi tuyến parabol với các sự dịch chuyển trong các biến không gian

M. I. Vishik, “On solvability of boundary-value problems for quasilinear parabolic equations of higher orders,” Mat. Sb. 59 (101) (supplementary), 289–325 (1962). J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites nonlinéaires (Dunod, Paris, 1969). Yu. A. Dubinskii, “Nonlinear elliptic and parabolic equations,” J. Soviet Math. 12, 475–554 (1979). H. Gajewski, K. Gröger, and K. Zaharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen (Akademie-Verlag, Berlin, 1974). I. V. Skrypnik, Methods for Studying Nonlinear Elliptic Boundary-Value Problems (Nauka. Fizmatlit, Moscow, 1990) [in Russian]. P. Hartman and G. Stampacchia, “On some nonlinear elliptic differential-functional equations,” Acta Math. 115, 271–310 (1966). O. V. Solonukha, “On nonlinear nonlocal parabolic problem,” Russ. J. Math. Phys. 29 (1), 121–140 (2022). A. L. Skubachevskii, “The first boundary value problem for strongly elliptic differential-difference equations,” J. Differential Equations 63 (3), 332–361 (1986). A. L. Skubachevskii, Elliptic Functional Differential Equations and Applications (Birkhäuser, Basel –Boston–Berlin, 1997). A. L. Skubachevskii, “Boundary-value problems for elliptic functional-differential equations and their applications,” Russian Math. Surveys 71 (5), 801–906 (2016). L. E. Rossovskii, “Elliptic functional differential equations with contractions and extensions of independent variables of the unknown function,” J. Math. Sci. New York 223 (4), 351–493 (2017). A. L. Skubachevskii, “Bifurcation of periodic solutions for nonlinear parabolic functional differential equations arising in optoelectronics,” Nonlinear Anal. 32 (2), 261–278 (1998). A. L. Skubachevskii and A. M. Selitskii, “The second boundary-value problem for parabolic differential-difference equations,” Russian Math. Surveys 62 (1), 191–192 (2007). A. B. Muravnik, “Functional differential parabolic equations: integral transformations and qualitative properties of solutions of the cauchy problem,” J. Math. Sci. New York 216, 345–496 (2016). O. V. Solonukha, “The first boundary value problem for quasilinear parabolic differential-difference equations,” Lobachevskii J. Math. 42 (5), 1067–1077 (2021). O. V. Solonukha, “On a class of essentially nonlinear elliptic differential-difference equations,” Proc. Steklov Inst. Math. 283, 226–244 (2013). Z. Guan, A. G. Kartsatos and I. V. Skrypnik, “Ranges of densely defined generalized pseudomonotone perturbations of maximal monotone operators,” J. Differential Equations 188 (1), 332–351 (2003). A. L. Skubachevskii, “Boundary value problems for differential-difference equations with incommensurable shifts,” Dokl. Math. 45 (3), 695–699 (1992). E. P. Ivanova, “Methods for studying differential-difference equations with incommensurable shifts of arguments,” in Proc. Voronezh Spring Mathematical School, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. i ee Prilozh. (VINITI RAN, Moscow, 2022), Vol. 204, pp. 44–52 [in Russian]. M. A. Krasnosel’skii, Topological Methods in the Theory of Nonlinear Integral Equations (Gostekhizdat, Moscow, 1956) [in Russian]. S. L. Sobolev, Some Applications of Functional Analysis in Mathematical Physics (Nauka, Moscow, 1988) [in Russian]. O. V. Solonukha, “On nonlinear and quasilinear elliptic functional-differential equations,” Discrete Contin. Dyn. Syst. Ser. S 9 (3), 847–868 (2016).