Displaying similar documents to “On the limit properties of the Picard singular integral.”

Improper Integral

Vladimir Janković (1998)

The Teaching of Mathematics


The existence of a solution and a numerical method for the Timoshenko nonlinear wave system

Jemal Peradze (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique


The initial boundary value problem for a beam is considered in the Timoshenko model. Assuming the analyticity of the initial conditions, it is proved that the problem is solvable throughout the time interval. After that, a numerical algorithm, consisting of three steps, is constructed. The solution is approximated with respect to the spatial and time variables using the Galerkin method and a Crank–Nicholson type scheme. The system of equations obtained by discretization is solved by...

A singular version of Leighton's comparison theorem for forced quasilinear second order differential equations

Ondřej Došlý, Jaroslav Jaroš (2003)

Archivum Mathematicum


We extend the classical Leighton comparison theorem to a class of quasilinear forced second order differential equations ( r ( t ) | x ' | α - 2 x ' ) ' + c ( t ) | x | β - 2 x = f ( t ) , 1 < α β , t I = ( a , b ) , ( * ) where the endpoints a , b of the interval I are allowed to be singular. Some applications of this statement in the oscillation theory of (*) are suggested.