Sentence examples for a continuously differentiable function from inspiring English sources

([6]) Let y : I → ℝ be a continuously differentiable function satisfying the differential inequality y ′ ( t ) + g ( t ) y ( t ) + h ( t ) ≤ φ ( t ). for all t ∈ I, where g, h : I → ℝ are continuous functions and φ : I → [0, ∞) is a function. Assume that.

Let (f:mathbb{R}^{m times n} to mathbb{R}) be a continuously differentiable function with Lipschitz continuous gradient and the Lipschitz constant (L ( f )).

Definition 3. A continuously differentiable function u satisfying the integro-differential equation (2). is called a mild solution of problem (1).

We are concerned with the oscillatory and nonoscillatory behavior of solutions of even-order quasilinear functional differential equations of the type, where and are positive constants, and are positive continuous functions on, and is a continuously differentiable function such that,.

If a continuously differentiable function (y : I to{mathbf{R}}) satisfies the differential inequality (2) for all (t in I), then there exists a solution (z : I to{mathbf{R}}) of the differential equation (1) such that biglvert y(t) - z(t) bigrvert leqfrac{varepsilon}{mu}quad textit{for all } t in I. (11).

An example is finding the maximum value of a continuously differentiable function f(x) defined in some interval a ≤ x ≤ b.

be a continuously differentiable function.

f is a continuously differentiable function.

Let φ be a continuously differentiable function on ([1,infty)).

Let be a continuously differentiable function with and on a compact subinterval of.

It is clear that h is a continuously differentiable function such that (h(0)) exists.