Sentence examples for coefficients are continuous from inspiring English sources

In the next theorem, let us consider the case that principal coefficients are continuous.

In the next theorem, we consider the case when principal coefficients are continuous.

be th-order linear differential equation whose coefficients are continuous on an interval.

The differential operator is called regular if its domain is finite and its coefficients are continuous, otherwise it is called a singular differential operator.

Montes de Oca and Zeeman [6] investigated the general nonautonomous -species Lotka-Volterra competitive system (1.2). and obtained that if the coefficients are continuous and bounded above and below by positive constants, and if for each there exists an integer such that (1.3).

We assume all the coefficients are continuous bounded nonnegative functions on R + = [ 0, + ∞ ). If f ( t ) is a continuous bounded function on R +, define f u = sup t ∈ R + f ( t ), f l = inf t ∈ R + f ( t ). Throughout this paper, suppose that a 2 l > 0, m i l > 0 ( i = 1, 2, 3 ), b i l > 0 ( i = 1, 2 ).

(2) If Ω is bounded and the coefficients (a_{ij}) are continuous, it is well known that problem (1) is uniquely solvable (see, for instance, the classical results in [1, 2]).

end{aligned}On the way to the existence of a weak solution, we first consider the stronger assumptions that all coefficient functions are continuous (w.r.t. both arguments) and not Carathéodory as assumed in Theorem 4.

In this case, if the coefficients are Lipschitz continuous and bounded the existence and uniqueness of a solution holds if H>d4.

Again we check that the drift and diffusion coefficients are Lipschitz continuous.

This problem is extremely complex when the coefficients are general continuous functions.