New bounds for solutions of a singular integro-differential inequality

Abstract

Abstract. New bounds for solutions of an integro-differential inequality with weakly singular kernel are established using a weighted version of the Hardy-Littlewood-Sobolev inequality. Besides, some applications to real world problems are presented.Mathematics subject classification (2010): 42B20, 26D07, 26D15.

A Nonlinear Weakly Singular Retarded Henry-Gronwall Type Integral Inequality and Its Application

“…and the estimates of solutions are given. From then on, more attention has been paid to such inequalities with singular kernel; see [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] and the references cited therein. Ye and Gao [20] considered the integral inequality of Henry-Gronwall type with delay…”

On Weakly Singular Versions of Discrete Nonlinear Inequalities and Applications

“…As for other new weakly singular inequalities, recent work can be found, for example, in [16][17][18][19][20][21][22][23][24][25] and references therein. In this paper, we investigate some new nonlinear discrete weakly singular inequalities…”

Some New Nonlinear Weakly Singular Inequalities and Applications to Volterra-Type Difference Equation

“…was discussed by Yang et al [11]. For other new weakly singular inequalities, lots of work can be found, for example, in [12][13][14][15][16][17][18][19][20][21][22] and references therein.…”