Asymptotics of slowly varying solutions of second-order differential equations with regularly and rapidly varying nonlinearities.

Regularly Varying Solutions of Second-Order Difference Equations with Arbitrary Sign Coefficient

Asymptotic Behavior of Intermediate Solutions of Fourth-order Nonlinear Differential Equations with Regularly Varying Coefficients

We study the fourth-order nonlinear differential equation ` p(t)|x′′(t)|α−1 x′′(t) ́′′ + q(t)|x(t)|β−1 x(t) = 0, α > β, with regularly varying coefficient p, q satisfying Z ∞ a t “ t p(t) ”1/α dt <∞. in the framework of regular variation. It is shown that complete information can be acquired about the existence of all possible intermediate regularly varying solutions and their accurate asymptoti...

Existence of Regularly and Rapidly Varying Solutions for a Class of Third Order Nonlinear Ordinary Differential Equations

The existence of solutions belonging to the Karamata class of functions of a class of third order nonlinear differential equations is proved via some more general results on asymptotic equivalence.

Regularly Varying Solutions of Perturbed Euler Differential Equations and Related Functional Differential Equations

An asymptotic analysis in the framework of Karamata regularly varying functions is performed for the solutions of second order linear differential and functional differential equations in the critical case i.e., when condition (1.5) as given below, holds.

Slowly Varying Solutions of a Class of First Order Systems of Nonlinear Differential Equations

We analyze positive solutions of the two-dimensional systems of nonlinear differential equations x′ + p(t)y = 0, y′ + q(t)x = 0, (A) x′ = p(t)y, y′ = q(t)x , (B) in the framework of regular variation and indicate the situation in which system (A) (resp. (B)) possesses decaying solutions (resp. growing solutions) with precise asymptotic behavior as t → ∞.