A problem with nonlocal conditions for mixed-type equations

Gulbakhor M. Mirsaburova

Chair of Differential Equations and Geometry, Termez State University, 43 F. Khodzhaev str., Termez, 190111 Republic of Uzbekistan

Abstract: We study a problem with Bitsadze–Samarskii conditions on a boundary of ellipticity and on a segment of line of degeneration with a condition of boundary characteristics of the Gellerstedt equation with singular coefficient. With the help of the maximum principle we prove uniqueness of a solution to the problem, and with the help of the method of integral equations we prove the existence of a solution to the problem.

Keywords: singular coefficient, uniqueness of solution to a problem, Wiener–Hopf equation, index of an equation.

UDC: 517.956

Received: 18.03.2013
Revised: 28.07.2013

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2014, 58:10, 29–35

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