On Stieltjes-Volterra integral equations
Copyright policy )On Stieltjes-Volterra integral equations
A Stieltjes-Volterra integral equation systemis firstly considered. Pointwise estimates and boundedness of its solutions are obtained under various conditions on the functionK. To do this, the well-known Gronwall-Bellman integral inequality is generalized. For a particular choice ofu, it is shown that the integral equation reduces to a difference equation. The problem of existence (and non-existence), uniqueness (and non-uniqueness) of the difference equation is discussed. Gronwall-Bellman inequality is further generalized tonlinear terms and is subsequently applied to obtain sufficient conditions in order that a certain stability of the unperturbed Volterra systemimplies the corresponding local stability of the (discontinuously) perturbed system
- Maharaja Bir Bikram University India
- University of Mumbai India
Systems of nonsingular linear integral equations, Approximation By Difference Equations, Volterra integral equations, Gronwall-Bellman Integral Inequality, Systems of Stieltjes-Volterra Integral Equations, Estimates of Solutions, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, Asymptotics of solutions to integral equations, Stability, Boundedness Of Solutions
Systems of nonsingular linear integral equations, Approximation By Difference Equations, Volterra integral equations, Gronwall-Bellman Integral Inequality, Systems of Stieltjes-Volterra Integral Equations, Estimates of Solutions, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, Asymptotics of solutions to integral equations, Stability, Boundedness Of Solutions
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