Asymptotic representations of the solutions with slowly varying derivatives of second order essential nonlinear differential equations
Journal Title: Дослідження в математиці і механіці - Year 2015, Vol 20, Issue 1
Abstract
The asymptotic representations, necessary and sufficient conditions of the existence of the solutions with slowly varying derivatives are found for differential equations of the second order that are in some sense similar to equations with nonlinearities, that are regularly varying at the singular points.
Authors and Affiliations
M. A. Bilozerova
About constant in Szego inequality for derivatives of conjugate trigonometric polynomials in L0.
We consider Szego inequality ˜ T(r) n 0 χ0 (n, r) ・ Tn 0 for derivatives of conjugate trigonometric polynomials in L0. We’ve found exact asymptotic by n estimation of constant χ0 (n, r) in it, improving estimates which...
Variational method of homogeneous solutions for axisymmetric elasticity problems
A variational method of homogeneous solutions for solving of axisymmetric elasticity problems for semiinfinite and finite cylinders with free lateral surface has been developed. As an example of application of the method...
To the theory of Hilbert space’s unconditional basis from values of entire vector-functions
Classes of entire functions of exponential type are considered in the article. They fulfil certain conditions related to theorems about unconditional basises from the values of entire vectorfunctions. In particular, for...
About the characteristic polynomial of product Frobenius’ matrix
The formula for calculating characteristic polynomials of product Frobenius’ matrix was obtained. The opportunity of using this formula by the tasks of control of nonlinear discret systems was shown.
Initial-boundary value problems for nonlinear parabolic equations with the variable exponents of nonlinearity and integral operators type Volterra
Initial-boundary value problems for nonlinear Volterra integro-differential equations with the variable exponents of nonlinearity are investigated. Weak solutions which belong to the generalized Sobolev and Lebesgue spac...