Some new integral inequalities with mixed nonlinearities for discontinuous functions

Abstract

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.

A class of dynamic integral inequalities with mixed nonlinearities and their applications in partial dynamic systems

“…3 generalize the results in [12][13][14] to two independent variables, which can be used to study the boundedness of dynamic systems.…”

“…For the study of time scales theory, integral inequalities are usually used to investigate the boundedness of dynamic systems. In recent years, different types of integral inequalities have been widely studied [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. For example, the sublinear integral inequality…”

“…was considered in [14], and the theoretical results can provide the bounds for a class of dynamic systems with mixed nonlinearities and impulsive effects. Very recently, Boudeliou [25] investigated a class of nonlinear integral inequalities in two independent variables and their applications.…”

A class of new nonlinear dynamic integral inequalities containing integration on infinite interval on time scales

“…where P(t), Q(t), and R(t) are defined as in (29), (30), and (31). By a similar argument with Theorem 3.1 in the rest of the proof, one can prove that (28).…”

Some Nonlinear Delay Volterra–Fredholm Type Dynamic Integral Inequalities on Time Scales

“…In recent years, many authors have been devoted to studying different kinds of integral inequalities and their applications [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24], especially the application of Volterra-Fredholm integrodifferential system [25][26][27][28]. To mention a few, in [8], Gu and Meng considered the nonlinear dynamic integral inequalities on time scales and applied the theoretical results to Volterra-Fredholm integrodifferential system, and Liu [9] investigated the linear delay Volterra-Fredholm type dynamic integral inequalities which generalized the main results of [8].…”