Asymptotic representations of solutions of essentially nonlinear cyclic systems of ordinary differential equations

Евтухов, В. М.; Vladova, E. S.

doi:10.1134/s0012266112050023

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2014

2015

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It would be of interest to prove a variant of Theorem 4.7 which ensures the existence of strongly decreasing slowly varying solutions for system (A). Related results on the existence of positive solutions with specific asymptotic behavior for a class of nonlinear differential systems which includes system (4.2) and which could be combined with perturbation techniques to produce some new results for system (A) can be found in [3].…”

Section: )mentioning

confidence: 99%

Existence and sharp asymptotic behavior of positive decreasing solutions of a class [4pt] of differential systems with power-type nonlinearities

Jaroš¹,

Kusano²

2014

Arch. Math. (Brno)

View full text Add to dashboard Cite

show abstract

Section: )mentioning

confidence: 99%

Existence and sharp asymptotic behavior of positive decreasing solutions of a class [4pt] of differential systems with power-type nonlinearities

Jaroš¹,

Kusano²

2014

Arch. Math. (Brno)

View full text Add to dashboard Cite

show abstract

Strongly increasing solutions of cyclic systems of second order differential equations with power-type nonlinearities

Jaroš¹,

Kusano²

2015

OpMath

View full text Add to dashboard Cite

Abstract. We consider n-dimensional cyclic systems of second order differential equationsunder the assumption that the positive constants αi and βi satisfy α1. . .αn > β1. . .βn and pi(t) and qi(t) are regularly varying functions, and analyze positive strongly increasing solutions of system ( * ) in the framework of regular variation. We show that the situation for the existence of regularly varying solutions of positive indices for ( * ) can be characterized completely, and moreover that the asymptotic behavior of such solutions is governed by the unique formula describing their order of growth precisely. We give examples demonstrating that the main results for ( * ) can be applied to some classes of partial differential equations with radial symmetry to acquire accurate information about the existence and the asymptotic behavior of their radial positive strongly increasing solutions.

show abstract

Asymptotic representations of solutions of essentially nonlinear cyclic systems of ordinary differential equations

Cited by 2 publications

References 2 publications

Existence and sharp asymptotic behavior of positive decreasing solutions of a class [4pt] of differential systems with power-type nonlinearities

Existence and sharp asymptotic behavior of positive decreasing solutions of a class [4pt] of differential systems with power-type nonlinearities

Strongly increasing solutions of cyclic systems of second order differential equations with power-type nonlinearities

Contact Info

Product

Resources

About