Asymptotic equivalence relations for rapidly varying solutions of sublinear differential equations of Emden–Fowler type
نویسندگان
چکیده
Abstract We discuss sublinear differential equations of the Emden–Fowler type $x''=q(t) x^{\gamma }$ x ″ = q ( t ) γ under assumption that coefficient q is a rapidly varying function. show all their strongly decreasing and increasing solutions are functions in asymptotic equivalence relation with precisely defined function determined by .
منابع مشابه
Asymptotic equivalence of differential equations and asymptotically almost periodic solutions
In this paper we establish asymptotic (biasymptotic) equivalence between spaces of solutions of a given linear homogeneous system and a perturbed system. The perturbations are of either linear or weakly linear characters. Existence of a homeomorphism between subspaces of almost periodic and asymptotically (biasymptotically) almost periodic solutions is also obtained.
متن کاملAsymptotic stability and asymptotic solutions of second-order differential equations
We improve, simplify, and extend on quasi-linear case some results on asymptotical stability of ordinary second-order differential equations with complex-valued coefficients obtained in our previous paper [G.R. Hovhannisyan, Asymptotic stability for second-order differential equations with complex coefficients, Electron. J. Differential Equations 2004 (85) (2004) 1–20]. To prove asymptotic stab...
متن کاملDifferential Delayed Equations - Asymptotic Behavior of Solutions and Positive Solutions
Brief Summary of Basic Notions For a b R , ∈ , a b < , let ([ ] ) n C a b R , , be the Banach space of the continuous functions from the interval [ ] a b , into n R equipped with the supremum norm | ⋅ | . In the case 0 a r = − < , 0 b = , we shall denote this space as r C , that is, ([ 0] ) n r C C r R := − , , and put 0 sup ( ) r r σ φ φ σ − ≤ ≤ || || = | | for r C φ∈ . If R σ ∈ , 0 A ≥ and ([...
متن کاملAsymptotic 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...
متن کاملIncreasing Solutions of Thomas-fermi Type Differential Equations – the Sublinear Case
A b s t r a c t. The existence and the asymptotic of solutions of the equations of Thomas-Fermi type is studied in the framework of regular variation (in the sense of Karamata).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Continuous and Discrete Models
سال: 2022
ISSN: ['2731-4235']
DOI: https://doi.org/10.1186/s13662-022-03693-w