Abstract
In this paper, some new nonlinear integral inequalities are established, which provide a handy tool for analyzing the global existence and boundedness of solutions of differential and integral equations. The established results generalize the main results in Sun (J. Math. Anal. Appl. 301, 265-275, 2005), Ferreira and Torres (Appl. Math. Lett. 22, 876-881, 2009), Xu and Sun (Appl. Math. Comput. 182, 1260-1266, 2006) and Li et al. (J. Math. Anal. Appl. 372, 339-349 2010). MSC 2010: 26D15; 26D10
Highlights
1 Introduction During the past decades, with the development of the theory of differential and integral equations, a lot of integral inequalities, for example [1,2,3,4,5,6,7,8,9,10,11,12], have been discovered, which play an important role in the research of boundedness, global existence, stability of solutions of differential and integral equations
Let u, f, g be nondecreasing continuous functions defined on R+ and let c be a nonnegative constant
Example 2: Considering the following integral equation β(y) α(x) u(x, y)ln(u(x, y) + 1) = a(x, y) +
Summary
With the development of the theory of differential and integral equations, a lot of integral inequalities, for example [1,2,3,4,5,6,7,8,9,10,11,12], have been discovered, which play an important role in the research of boundedness, global existence, stability of solutions of differential and integral equations.In [9], the following two theorems for retarded integral inequalities were established. In [9], the following two theorems for retarded integral inequalities were established. Let φ ∈ C(R+0, R+0) be a strictly increasing function such that lim φ(x) = ∞
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