Solutions of many applied Cauchy problems for ordinary differential equations have one or more multiple zeros on the integration segment. Examples are special functions mathematical physics. The presence multiples significantly complicates numerical calculation, since such ill-conditioned. Round-off errors may corrupt all decimal digits solution. Therefore, should be treated as points equations...

We establish the local and global theory for Cauchy problem of singular Hartree equation in three dimensions, that is, modification non-linear Schrodinger with n...

This paper presents an analytical solution for an orthotropic circular cross section bar with a magnetic coating weakened by multiple arbitrary oriented cracks under Saint-Venant torsion by means of the distributed dislocation technique. At first, the solution of the orthotropic bar with a magnetic coating weakened by a Volterra-type screw dislocation is achieved with the aid of the finite Four...

We study the Cauchy problem for 22 semilinear and quasilinear hyperbolic systems with a singular relaxation term. Special comparison and compactness properties are established by assuming the subcharacteristic condition. Therefore we can prove the convergence to equilibrium of the solutions of these problems as the singular perturbation parameter tends to zero. This research was strongly motiva...

Abstract: The solution to problem of an orthotropic long cylinder subjected to torsional loading is first obtained by means of separation valuables. The cylinder is twisted by two lateral shear tractions and the ends of the cylinder surface of the cylinder are stress-free. First, the domain under consideration is weakened by an axisymmetric rotational Somigliana ring dislocation. The dislocatio...