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Asymptotic forms of solutions of perturbed half-linear ordinary differential equations

Sokea Luey, Hiroyuki Usami (2021)

Archivum Mathematicum

Asymptotic forms of solutions of half-linear ordinary differential equation ( | u ' | α - 1 u ' ) ' = α ( 1 + b ( t ) ) | u | α - 1 u are investigated under a smallness condition and some signum conditions on b ( t ) . When α = 1 , our results reduce to well-known ones for linear ordinary differential equations.

Asymptotic relationship between solutions of two linear differential systems

Jozef Miklo (1998)

Mathematica Bohemica

In this paper new generalized notions are defined: Ψ -boundedness and Ψ -asymptotic equivalence, where Ψ is a complex continuous nonsingular n × n matrix. The Ψ -asymptotic equivalence of linear differential systems y ' = A ( t ) y and x ' = A ( t ) x + B ( t ) x is proved when the fundamental matrix of y ' = A ( t ) y is Ψ -bounded.

Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria

Felipe Alvarez, Hedy Attouch (2001)

ESAIM: Control, Optimisation and Calculus of Variations

It is established convergence to a particular equilibrium for weak solutions of abstract linear equations of the second order in time associated with monotone operators with nontrivial kernel. Concerning nonlinear hyperbolic equations with monotone and conservative potentials, it is proved a general asymptotic convergence result in terms of weak and strong topologies of appropriate Hilbert spaces. It is also considered the stabilization of a particular equilibrium via the introduction of an asymptotically...

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