scholarly journals Conditional Stability and Asymptotic Behavior of Solutions of Weakly Delayed Linear Discrete Systems in R2

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Josef Diblík ◽  
Hana Halfarová ◽  
Jan Šafařík
Keyword(s):  
Asymptotic Behavior ◽  
Discrete Systems ◽  
Asymptotic Formulas ◽  
Asymptotic Behavior Of Solutions ◽  
Conditional Stability ◽  
Two Dimensional ◽  
Linear Discrete Systems

Two-dimensional linear discrete systems x(k+1)=Ax(k)+∑l=1nBlxl(k-ml),  k≥0, are analyzed, where m1,m2,…,mn are constant integer delays, 0<m1<m2<⋯<mn, A, B1,…,Bn are constant 2×2 matrices, A=(aij), Bl=(bijl),  i,j=1,2,  l=1,2,…,n, and x:{-mn,-mn+1,…}→R2. Under the assumption that the system is weakly delayed, the asymptotic behavior of its solutions is studied and asymptotic formulas are derived.

Asymptotic behavior of solutions of half-linear differential equations and generalized Karamata functions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kusano Takaŝi ◽  
Jelena V. Manojlović
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Continuous Function ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Regular Variation ◽  
Asymptotic Formulas ◽  
Asymptotic Behavior Of Solutions ◽  
Positive Continuous Function ◽  
Linear Differential

AbstractWe study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation(p(t)\lvert x^{\prime}\rvert^{\alpha}\operatorname{sgn}x^{\prime})^{\prime}+q(% t)\lvert x\rvert^{\alpha}\operatorname{sgn}x=0,where q is a continuous function which may take both positive and negative values in any neighborhood of infinity and p is a positive continuous function satisfying one of the conditions\int_{a}^{\infty}\frac{ds}{p(s)^{1/\alpha}}=\infty\quad\text{or}\quad\int_{a}^% {\infty}\frac{ds}{p(s)^{1/\alpha}}<\infty.The asymptotic formulas for generalized regularly varying solutions are established using the Karamata theory of regular variation.

An asymptotic analysis for Hamilton–Jacobi equations with large Hamiltonian drift terms

2017 ◽  
Vol 0 (0) ◽  
Author(s):  
Taiga Kumagai
Keyword(s):  
Asymptotic Behavior ◽  
Euclidean Space ◽  
Asymptotic Analysis ◽  
Open Subset ◽  
Dimensional Euclidean Space ◽  
Asymptotic Behavior Of Solutions ◽  
Two Dimensional ◽  
Jacobi Equations ◽  
Drift Terms

AbstractWe investigate the asymptotic behavior of solutions of Hamilton–Jacobi equations with large Hamiltonian drift terms in an open subset of the two-dimensional Euclidean space. The drift is given by

Fault Diagnosability Analysis of Two-Dimensional Linear Discrete Systems

2020 ◽  
pp. 1-1
Author(s):  
Dong Zhao ◽  
Choon Ki Ahn ◽  
Wojciech Paszke ◽  
Fangzhou Fu ◽  
Yueyang Li
Keyword(s):  
Discrete Systems ◽  
Two Dimensional ◽  
Linear Discrete Systems ◽  
Fault Diagnosability

scholarly journals Asymptotic Behavior of Solutions of the Dirac System with an Integrable Potential

2021 ◽  
Vol 93 (5) ◽  
Author(s):  
Łukasz Rzepnicki
Keyword(s):  
Asymptotic Behavior ◽  
Spectral Parameter ◽  
Asymptotic Formulas ◽  
Asymptotic Behavior Of Solutions ◽  
Dirac System ◽  
Eigenvalues And Eigenfunctions ◽  
Integrable Potential ◽  
Sturm Liouville ◽  
Complex Valued ◽  
Liouville Operators

AbstractWe consider the Dirac system on the interval [0, 1] with a spectral parameter $$\mu \in {\mathbb {C}}$$ μ ∈ C and a complex-valued potential with entries from $$L_p[0,1]$$ L p [ 0 , 1 ] , where $$1\le p$$ 1 ≤ p . We study the asymptotic behavior of its solutions in a strip $$|\mathrm{Im}\,\mu |\le d$$ | Im μ | ≤ d for $$\mu \rightarrow \infty $$ μ → ∞ . These results allow us to obtain sharp asymptotic formulas for eigenvalues and eigenfunctions of Sturm–Liouville operators associated with the aforementioned Dirac system.

Sign in / Sign up

Export Citation Format

Share Document