ASYMPTOTIC REPRESENTATIONS OF SOLUTIONS WITH SLOWLY VARYING DERIVATIVES
Journal Title: Дослідження в математиці і механіці - Year 2018, Vol 23, Issue 2
Abstract
Second-order differential equations with power and exponential nonlinearities on the right hand side play an important role in the development of a qualitative theory of differential equations. The authors of most works devoted to the establishment of asymptotic representations of solutions investigate equations with power and with regularly varying nonlinearities. Recently, the consideration of differential equations with exponential and a wider class than exponential functions - rapidly varying functions - has begun. In this paper, the asymptotic representations of solutions with slowly varying first-order derivatives of some new class of second-order differential equations with rapidly and regularly varying nonlinearities are established.
Authors and Affiliations
O. O. Chepok
Keywords
Related Articles
- EP ID EP558809
- DOI 10.18524/2519-206x.2018.2(32).149708
- Views 89
- Downloads 0
Stieltjes integral and summation formula
In the article we prove a generalized summation formula using the expanded definition of the Stieltjes integral.
Comparison of error indicators and refinement criteria for hp-adaptation algorithm for finite element method
In this paper we consider hp-adaptive finite element method for 1D convection-diffusion-advection boundary value problem and present comparative analysis of numerical results obtained using combination of introduced algo...
GENERALIZATIONS OF UNIVERSALITY FOR PERIODIC HURWITZ ZETA FUNCTIONS
It is well known that zeta-functions universal in the sense that their shifts uniformly on compact subsets of some region approximate any analytic functions form a rather wide class. In the paper, the universality for co...
Asymptotic representations of the solutions with slowly varying derivatives of second order essential nonlinear differential equations
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 simila...
Conditions of existence and uniqueness of solutions for set-valued Volterra integral equation
In 1969, F. S. de Blasi and F. Iervolino examined set-valued differential equation (differential equation with derivative Hukuhara). In the future, many authors have studied the question of the existence, uniqueness and...