This article is cited in 5 papers

Problems with shifts for mixed elliptic-hyperbolic equations

M. Kh. Ruziev

Department of Differential Equations, Institute of Mathematics and Information Technologies, Uzbekistan Academy of Sciences, Tashkent, Republic of Uzbekistan

Abstract: In this paper we study a problem with a shift, where some characteristics are free from boundary conditions; the absent V. I. Zhegalov and A. M. Nakhushev conditions are replaced with an analog of F. Frankl condition on a segment of the degeneration line. We prove the unique solvability of the mentioned problem with the help of the extremum principle. The proof of the solvability is based on the theory of singular integral equations, Wiener–Hopf equations and Fredholm integral equations.

Keywords: principle of extremum, unique solvability, solvability, singular coefficient, integral equations, index of equation.

UDC: 517.956

Received: 28.12.2010

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:1, 66–75

Bibliographic databases:

• 
•