Sentence examples for continuous dependence from inspiring English sources
Uniqueness and continuous dependence results are presented.
First, we prove existence, uniqueness and continuous dependence with respect to the initial condition of solutions.
Stability and invariance results are also studied, together with the property of continuous dependence on the initial conditions.
We also establish the continuous dependence with the perturbation of the constants in the notion of dichotomy.
Our method is based on the implicit function theorem which yields necessarily continuous dependence of solutions for the initial data.
Topics for ordinary differential equations may include initial-value and two-point boundary value problems, the basic existence and uniqueness theorems, continuous dependence on data, stability of fix-points, numerical methods, special functions.
Topics for partial differential equations may include the Poisson, heat and wave equations, boundary and initial-boundary value problems, maximum principles, continuous dependence on data, separation of variables, Fourier series, Green's functions, numerical methods, transform methods.
To support interactive editing of a quadratic objective function, the stability of the model (the continuous dependence of the output ordinal preference on the input data) is proved.
Corollary 2.2 (Continuous dependence).
Theorem 3.5 (Continuous dependence).
