Journal of Samara State Technical University, Ser. Physical and Mathematical SciencesJournal of Samara State Technical University, Ser. Physical and Mathematical Sciences1991-86152310-7081Samara State Technical University6162610.14498/vsgtu1822Research ArticleOn a nonlocal boundary-value problem for a loaded parabolic-hyperbolic equation with three lines of degeneracyIslomovBozor I.<p>Dr. Phys. & Math. Sci., Professor; Chief Researcher; Dept. of Differential Equations and Mathematical Physics</p>islomovbozor@yandex.comhttps://orcid.org/0000-0002-4372-395XXolbekovJurat A.<p>Assistant; Dept. of Higher Mathematics</p>xolbekovja@mail.ruhttps://orcid.org/0000-0002-1495-2761National University of Uzbekistan named after M. UlugbekTashkent State Technical University named after I. Karimov300920212534074222302202128062021Copyright © 2021, Authors; Samara State Technical University (Compilation, Design, and Layout)2021<p>The work is devoted to the proof of the uniqueness and existence of a solution of a nonlocal problem for a loaded parabolic-hyperbolic equation with three lines of change of type. Using the representation of the general solution, the uniqueness of the solution is proved, and the existence of the solution is proved by the method of integral equations. Necessary conditions for the parameters and specified functions are established for the unique solvability of Volterra integral equations of the second kind with a shift equivalent to the problem under study.</p>loaded equationnonlocal problemVolterra integral equation with a shiftGreen's functionuniqueness and existence of a solutionнагруженное уравнениенелокальная задачаинтегральное уравнение Вольтерра со сдвигомфункция Гринаединственность и существование решения[Nakhushev A. M. 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