On the boundedness of a class of nonlinear dynamic equations of second order

On some new integral inequalities of Gronwall–Bellman–Bihari type with delay for discontinuous functions and their applications

“…The 2 celebrated results given by Gronwall, Bellman, Bihari and their linear and nonlinear generaliza-Q2 3 tions in the case of continuous and discontinuous functions provide a fundamental role in the 4 study of many qualitative properties of differential and integral equations, which we can find in 5 [3,6,4,11,12,15-17,2, 1,10,9]. For some new development on this topic, see [5,8,13,18,14,19,7]. 6 In 2007, Jiang and Meng [8] discussed the following delay integral inequalities:…”

“…Assume that x(t), ρ(t), π(t), σ (t) are defined in Theorem 2.1 and x(t) satisfies 13 the following form of integral inequality 14 x p (t) ≤ ρ(t) + π(t)…”

Reconstruction of nonlinear integral inequalities associated with time scales calculus

“…Over the most recent couple of years, great efforts have been made to unify and expand integral inequalities on time scales [5][6][7][8][9][10][11][12]. These essential inequalities are promoted in numerous classifications for the boundedness, uniqueness, and the solutions of various dynamic equations [13][14][15][16].…”

Some inequalities for Csiszár divergence via theory of time scales

“…Many authors established time scale version of linear and nonlinear integral inequalities [1,17,19]. The time scale integral inequalities have been used to study the boundedness, uniqueness, and so on of the solutions of different dynamic equations [14,16]. Ansari et al [2] introduced the differential entropy of a continuous random variable on time scales and established some Shannon-type inequalities on arbitrary time scales.…”