Partial Differential Equations


The local extremum principle for a hyperbolic equation and its application V. F. Volkodavov, N. Ya. Nikolaev

3 

On the question of the necessary condition for the stabilization of the solution of the Cauchy problem for a heat equation that is uniform on any compactum V. N. Denisov

7 

The general solution of a system of partial differential equations V. S. Zhgenti, A. R. Hvoles

17 

Relations that are exact with respect to order between $L_2$norms of eigen and associated functions of a secondorder elliptic operator V. A. Il'in

30 

Regular extensions of the semiminimal Lavrent'ev–Bitsadze operator T. Sh. Kal'menov

37 

On the uniqueness of the solution of some boundary value problems for equations of mixed type and for hyperbolic equations in $m$dimensional space G. D. Karatoprakliev

59 

On the completeness of eigenelements of some nonlinear equations A. P. Makhmudov

64 

An approximate method for solving boundary value problems for differential equations and its application to the dynamics of ground moisture and ground water A. M. Nakhushev

72 

A problem of Tricomi type for the Lavrent'ev–Bitsadze equation in a domain with an infinite set of characteristic triangles Ch. T. Nguyen

81 

A problem with displacement for a hyperbolic equation with noncharacteristic degeneration on part of the boundary I. Orazov

92 

On the solvability of some higherorder quasilinear elliptic equations S. I. Pokhozhaev

100 

Some new results of the theory of regularized traces of differential operators V. A. Sadovnichii, V. A. Lyubishkin

109 

Two nonlocal boundary value problems for a degenerate hyperbolic equation M. S. Salakhitdinov, M. Mirsaburov

116 

On a class of singular integral operators on the line with onesided shift A. P. Soldatov

127 

The Cauchy problem for differential equations with constant coefficients in a half space in a class of generalized functions N. E. Tovmasyan

132 

Some properties of Euler fields O. V. Troshkin

138 

On a problem with an oblique fractional derivative for the Holmgren equation M. A. Usanetashvili

144 

On a Goursattype problem for a class of systems of secondorder equations of hyperbolic type S. S. Kharibegashvili

152 

Integral representation of $p$analytic functions with characteristic $p=e^{\lambda x}y^k$ D. Z. Khoang

166 

Short Communications


A solution in closed form of the Volterra equation with a hypergeometric function in the kernel M. M. Smirnov

171 

Boundary value problems for a threedimensional equation of mixed type of the second kind N. G. Sorokina

173 

Estimates of Wiman–Valiron type for solutions of differential equations N. M. Suleimanov

176 