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On fixed sign solution to nonhomogeneous equation of mixed parabolic-hyperbolic type of higher order

K. B. Sabitov<sup>abc

a</sup> Sterlitamak branch of Bashkir State University, 31 Lenin Ave., Sterlitamak, 453103 Russia
^b Sterlitamak branch of the Institute of for Strategic Studies of Bashkortostan Republic, 68 Odesskaya str., Sterlitamak, 453103 Russia
^c Institute of Applied Research of Bashkortostan Republic, 68 Odesskaya str., Sterlitamak, 453103 Russia

Abstract: For polycaloric equation and mixed parabolic-hyperbolic equation of the second order we ascertain a fixed sign solution depending on the right-hand side. Then, based on these results for the non-homogeneous equation of mixed parabolic-hyperbolic type of higher order, we invetsigate a fixed sign solution depending on the right-hand side.

Keywords: polycaloric equation, mixed parabolic-hyperbolic type of second and higher orders, maximum principle, fixed sign solution.

UDC: 517.957

Received: 18.03.2016

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:7, 49–57

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