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

Abstract

Some new nonlinear weakly singular difference inequalities are discussed, which generalize some known weakly singular inequalities and can be used in the analysis of nonlinear Volterra-type difference equations with weakly singular kernel. An application to the upper bound of solutions of a nonlinear difference equation is also presented.

Some New Generalized Retarded Gronwall-Like Inequalities and Their Applications in Nonlinear Systems

“…Recently, the celebrated Gronwall inequality and its generalizations play increasingly important roles in the qualitative analysis of differential, integral, and integrodifferential equations. Based on the different purposes, many researchers put their efforts in exploring new inequalities and their applications in many fields, and many useful Gronwall-like integral inequalities have been established in various problems (see [4][5][6][7][8][9][10][11][12][13][14][15][16][17]).…”