Sentence examples for solutions under perturbation from inspiring English sources
One usually concerns the existence of special kind of persistent solutions under perturbation.
This kind of well-posedness is a blending of Hadamard and Tikhonov notions, and it gives also links to stability theory and seems well adapted to describe the behaviors of solutions under perturbations.
Our aim is to establish the existence of periodic solutions under periodic perturbation and multiple variable lags.
For arbitrary α∈[0,1], we are interested in the solution of (38) under perturbation Δ α :=α Δ + (1−α)Δ ′.
The potentiodynamic behaviour of iron in alkaline solutions under carefully controlled perturbation conditions reveals that the overall electrochemical process is more involved than was thought earlier.
In one extreme, convergence to very different solutions under slight data perturbation that make no biological sense would indicate a problem in the modeling approach or with the ability to overcome local minima, while, on the other hand, consistent convergence to a single solution would suggest a distinct global optimum under the modeling assumptions.
In particular, he proved the solvability of these problems for nonlinear differential equations and systems with right-hand sides rapidly increasing with respect to the phase variable, introduced the notion of a strong isolated solution of a nonlinear problem, proved the stability of such a solution under small perturbations of the differential system.
proved the existence and uniqueness of solution of Duffing equations under perturbation functions and other conditions at nonresonance by employing minimax theorems.
We first discuss parameter dependence of stable mild solutions under sufficiently small Lipschitz perturbation in the parameter space Y.
We first discuss parameter dependence of stable mild solutions under sufficiently small Lipschitz perturbation in the parameter space Y. .
We consider p ( p ≥ 2 ) th moment locally exponential stability as well as almost surely exponential stability of mild solutions under sufficiently small nonlinear perturbations and sufficiently small initial value.
