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

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Kelong Zheng ◽  
Wenqiang Feng ◽  
Chunxiang Guo
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Upper Bound ◽  
Singular Kernel ◽  
Nonlinear Difference Equation ◽  
Volterra Type ◽  
Weakly Singular Kernel ◽  
Weakly Singular

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.

scholarly journals On Weakly Singular Versions of Discrete Nonlinear Inequalities and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Kelong Cheng ◽  
Chunxiang Guo ◽  
Qingke Zeng
Keyword(s):  
Difference Equations ◽  
Upper Bound ◽  
Nonlinear Difference Equations ◽  
Uniqueness Of Solutions ◽  
Volterra Type ◽  
Weakly Singular Kernels ◽  
Weakly Singular ◽  
Singular Kernels

Some new weakly singular versions of discrete nonlinear inequalities are established, which generalize some existing weakly singular inequalities and can be used in the analysis of nonlinear Volterra type difference equations with weakly singular kernels. A few applications to the upper bound and the uniqueness of solutions of nonlinear difference equations are also involved.

scholarly journals On the functional-integral equation of Volterra type with weakly singular kernel

2008 ◽  
Vol 83 (97) ◽  
pp. 57-63
Author(s):  
Aldona Dutkiewicz
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Sufficient Conditions ◽  
Functional Integral ◽  
Singular Kernel ◽  
Volterra Type ◽  
Weakly Singular Kernel ◽  
Measures Of Noncompactness ◽  
Weakly Singular

We give sufficient conditions for the existence of Lp-solution of a Volterra functional-integral equation in a Banach space. Our assumptions and proofs are expressed in terms of measures of noncompactness.

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