一类推广的非线性Volterra-Fredholm型积分不等式解的估计及其应用（英文）

Estimation on solutions of a class of generalized nonlinear Volterra-Fredholm type integral inequalities with applications

研究了一类新的非线性时滞Volterra-Fredholm型积分不等式.该不等式把文献[Ma,QH,Pecaric,J:Estimates on solutions of some new nonlinear retarded Volterra-Fredholm type integral inequalities.Nonlinear Anal.69(2008)393-407]中的函数σ_1(s)推广成函数w(u(s))f(s),其中w(u(s))是未知函数与非线性函数的复合函数.利用变量替换、放大及常量与变量的辩证关系等方法给出了该不等式中未知函数的估计.最后,用所得结果给出了一类积分方程解的估计.

We establish a class of new nonlinear retarded Volterra-Fredholm type integral inequalities, where a known function σ1（s） in integral functions in [Ma, QH, Pecari′c, J： Estimates on solutions of some new nonlinear retarded Volterra-Fredholm type integral inequalities. Nonlinear Anal. 69（2008） 393-407] is changed into the function w（u（s））f（s）, where w（u（s）） is the composite function of the unknown function u（s） and a nonlinear function w（u）. By adopting novel analysis techniques, such as： change of variable, amplification method, differential and integration, inverse function, and the dialectical relationship between constants and variables, the upper bounds of the embedded unknown functions are estimated explicitly. The derived results can be applied in the study of solutions of a class of integral equations.