Sentence examples for mixed nonlinearities of from inspiring English sources
We consider the second-order forced nonlinear dynamic equations containing mixed nonlinearities of the form (11). with (12).
This paper is concerned with some oscillation criteria for the second order neutral delay dynamic equations with mixed nonlinearities of the form where and with.
Motivated by the above observation, in this paper we consider the following second order neutral delay dynamic equation with mixed nonlinearities of the form: (1.6).
Moreover, for the special case we obtain interval oscillation criteria for difference equations with mixed nonlinearities of the form (111). for which almost nothing is available in the literature.
Our motivation in this study stems from the work contained in [34], where the authors have derived interval criteria for oscillation of second-order differential equations with mixed nonlinearities of the form (19). with (110).
We obtain new oscillation criteria for second-order forced dynamic equations on time scales containing mixed nonlinearities of the form, with,, where is a time scale interval with, the functions are right-dense continuous with, is the forward jump operator,, and.
Our results include many known ones in the literature and can be used as tools in the study of qualitative theory of certain classes of dynamic equations with mixed nonlinearities on time scales.
In this paper, we establish some new integral inequalities with mixed nonlinearities for discontinuous functions, which provide a handy tool in deriving the explicit bounds for the solutions of impulsive differential equations and differential-integral equations with impulsive conditions.
For example, the idea to interval oscillation in [25 29] and the idea of dealing with mixed nonlinearities in [22].
We study oscillatory behavior of a class of second-order forced differential equations with mixed nonlinearities.
Moreover the oscillatory behavior of solutions of second order differential and dynamic equations with mixed nonlinearities is discussed in [9 16].
