Rapidly varying solutions of a second-order differential equation with regularly and rapidly varying nonlinearities

We discuss sublinear differential equations of the Emden–Fowler type $x''=q(t) x^{\gamma }$ x ″ = q ( t ) x γ under the assumption that the coefficient q is a rapidly varying function. We show that all of their strongly decreasing and strongly increasing solutions are rapidly varying functions and are in the asymptotic equivalence relation with a precisely defined function determined by the coefficient q.

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Asymptotic behavior of some types of solutions of differential equations with different types of nonlinearities

Kolun

2020

Mat. Met. Fiz. Mekh. Polya

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Rapidly varying solutions of a second-order differential equation with regularly and rapidly varying nonlinearities

Cited by 5 publications

References 8 publications

Asymptotic Behavior of Some Types of Solutions of Differential Equations with Different Types of Nonlinearities

Asymptotic Behavior of Some Types of Solutions of Differential Equations with Different Types of Nonlinearities

Asymptotic equivalence relations for rapidly varying solutions of sublinear differential equations of Emden–Fowler type

Asymptotic behavior of some types of solutions of differential equations with different types of nonlinearities

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