Sentence examples for depending on the derivative from inspiring English sources

Many multiplicity results were obtained with the method of strict lower and upper solutions and for problems with the right member being a Carathéodory map not depending on the derivative, f ( t, u ).

where f : [ 0, ∞ [ × R × R → R is a given function, 2 < q < 3, α > 0, D 0 + q c denotes the Caputo fractional derivative. Note that few papers in the literature dealing with fractional differential equations considered the nonlinearity f in (P) depending on the derivative of u.

Conditions are given to characterize neutral systems with delays for which linear observers exist not depending on the derivatives of the state.

Furthermore, the variances (34) depend on the derivative of the CRF, which is to be estimated!

From Figures 1 and 2, it is easy to conclude that the solution continuously depends on the derivative.

We discuss a non-local boundary value problem of second-order, where the involved nonlinearity depends on the derivative and may be singular.

The advantage of representing a solution of the initial problem (1.1), (1.2) as a solution of (2.6) is that, although (2.6) remains to be a neutral system, its right-hand side does not explicitly depend on the derivative for depending only on the derivative of the initial function on the initial interval.

Moreover, the plasma E2 profiles observed depended on the derivative of oestradiol administered.

We propose new semiparametric estimators for parameters that depend on the derivatives (up to any finite order) of unknown conditional expectations and densities.

We also specify a general set of regularity conditions that contains a new restriction on the kernel function to avoid bias in the case that the parameter depends on the derivatives of the conditional expectation or density.

We use a class of multiplicative algorithms, indexed by a function f, which depends on the derivatives of the criterion function.