Volterra-stieltjes integral operators
Copyright policy )Volterra-stieltjes integral operators
The authors show that, under suitable growth and monotonicity assumptions on the data, the Volterra-Stieltjes integral operator \[ Vx(t) =\int^t_0v\bigl(s,x(s) \bigr)\,ds\,g(t,s)\quad (0\leq t\leq 1) \] maps the space \(C[0,1]\) into the space \(BV[0,1]\) (resp. \(BV[0,1]\cap C[0,1])\) and is both continuous and compact. This allows them to prove existence, through Schauder's fixed point theorem, of continuous monotone solutions \(x\) of the equation \(x=p+Vx\).
- Rzeszów University of Technology Poland
- University of Galway Ireland
Integral operators, Other nonlinear integral equations, Externally hosted open access publications with University of Galway authors, Compact operator, stieltjes integral, Volterra-Stieltjes integral operator, Function of bounded variation, compact operator, integral operator, function of bounded variation, Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.), Computer Science Applications, Fixed-point theorems, Continuous monotone solutions, monotonic function, Modelling and Simulation, equations, Monotonic function
Integral operators, Other nonlinear integral equations, Externally hosted open access publications with University of Galway authors, Compact operator, stieltjes integral, Volterra-Stieltjes integral operator, Function of bounded variation, compact operator, integral operator, function of bounded variation, Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.), Computer Science Applications, Fixed-point theorems, Continuous monotone solutions, monotonic function, Modelling and Simulation, equations, Monotonic function
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