Singular Cauchy problem for the general Euler-Poisson-Darboux equation

In this paper we obtain the solution of the singular Cauchy problem for the Euler-Poisson-Darboux equation when differential Bessel operator acts by each variable.

Solution of the singular Cauchy problem for a general inhomogeneous Euler–Poisson–Darboux equation

In this paper, we solve Cauchy problem for a general form of an inhomogeneous Euler–Poisson–Darboux equation, where Bessel operator acts instead of the each second derivative. In the classical formulation, the Cauchy problem for this equation is not correct. However, for a specially selected form of the initial conditions, the equation has a solution. The general form of the Euler–Poisson–Darboux equation with such conditions we will call the singular Cauchy problem.

ON SOLVABILITY OF SINGULAR CAUCHY PROBLEM FOR FUNCTIONAL DIFFERENTIAL EQUATION WITH SPECIAL TYPE DEVIATION

At this paper unique solvability conditions of singular at independent variable linear first order functional-differential equation with special type argument deviation and singular coefficient were obtained.