Inequalities of solutions of Volterra integral and differential equations.
Infinite systems of first order PFDEs with mixed conditions
We consider mixed problems for infinite systems of first order partial functional differential equations. An infinite number of deviating functions is permitted, and the delay of an argument may also depend on the spatial variable. A theorem on the existence of a solution and its continuous dependence upon initial boundary data is proved. The method of successive approximations is used in the existence proof. Infinite differential systems with deviated arguments and differential integral systems...
Initial and boundary value problems for functional integro-differential equations.
Initial value problems for integro-differential equations of Volterra type in Banach spaces.
Integrable and continuous solutions of a nonlinear quadratic integral equation.
Integrable solutions of a functional-integral equation.
This paper contains a theorem on the existence of monotonic and integrable solutions of a functional-integral equation. The proof of that theorem is based on the technique associated with the notion of a measure of weak noncompactness.
Integral equations and boundary value problems for eliptic partial differential equations
Integral equations and time varying linear systems.
In this paper we study the resolution problem of an integral equation with operator valued kernel. We prove the equivalence between this equation and certain time varying linear operator system. Sufficient conditions for solving the problem and explicit expressions of the solutions are given.
Integral equations of convolution type with power nonlinearity
Integral equations of the first kind of Sonine type.
Integral equations of the third kind
Integral equations via saddle point problem for 2D electromagnetic problems
Integral Equations VIA Saddle Point Problem for 2D Electromagnetic Problems
A new system of integral equations for the exterior 2D time harmonic scattering problem is investigated. This system was first proposed by B. Després in [11]. Two new derivations of this system are given: one from elementary manipulations of classical equations, the other based on a minimization of a quadratic functional. Numerical issues are addressed to investigate the potential of the method.
Integral equations, Volterra equations, and the remarkable resolvent: contractions.
Integral equations with contrasting kernels.
Integral inequalities of Gronwall type for piecewise continuous functions.
Integral operators and absolute convergence systems.
Integral operators generated by Mercer-like kernels on topological spaces
We analyze some aspects of Mercer's theory when the integral operators act on L²(X,σ), where X is a first countable topological space and σ is a non-degenerate measure. We obtain results akin to the well-known Mercer's theorem and, under a positive definiteness assumption on the generating kernel of the operator, we also deduce series representations for the kernel, traceability of the operator and an integration formula to compute the trace. In this way, we upgrade considerably similar results...
Integral Perturbations of Nonlinear Systems of Differential Equations
Integral repesentations and its applications in Clifford analysis.