Related papers: Nonconvolution nonlinear integral Volterra equatio…
In this paper the problems of integrable and linearizable Lotka-Volterra equations with $(\delta:-3 \delta:\delta)$-resonance are studied. The necessary conditions for both problems are obtained in the case when $\delta=1$ and it's…
Integral operators play an important role modeling various physical and biological processes. In this article we consider such a nonlinear integro-differential equation. We study several properties of equilibrium solutions of the operator…
In this paper we study a class of quadratic operators named by Volterra operators on infinite dimensional space. We prove that such operators have infinitely many fixed points and the set of Volterra operators forms a convex compact set. In…
In this paper, we are concerned with stochastic Volterra equations with singular kernels and H\"older continuous coefficients. We first establish the well-posedness of these equations by utilising the Yamada-Watanabe approach. Then, we aim…
We consider an inverse problem for the Boltzmann equation with nonlinear collision operator in dimensions $n\geq 2$. We show that the kinetic collision kernel can be uniquely determined from the incoming-to-outgoing mappings on the boundary…
We offer a simple method Monte Carlo for computation of Volterra's and spherical type multiple integrals with weak (integrable) singularities. An elimination of infinity of variance is achieved by incorporating singularities in the density,…
Two different Sinc-collocation methods for Volterra integral equations of the second kind have been independently proposed by Stenger and Rashidinia--Zarebnia. However, their relation remains unexplored. This study theoretically examines…
In this study we consider perturbative series solution with respect to a parameter {\epsilon} > 0. In this methodology the solution is considered as an infinite sum of a series of functional terms which usually converges fast to the exact…
This paper investigates two classes of quasilinear and essentially nonlinear integral equations with a sum-difference kernel on the half-line. Such equations arise in various areas of physics, including the theory of radiative transfer in…
The paper presents a collection of results on continuous dependence for solutions to nonlocal problems under perturbations of data and system parameters. The integral operators appearing in the systems capture interactions via heterogeneous…
We consider here convolution operators, in the Caputo sense, with non-singular kernels. We prove that the solutions to some integro-differential equations with such operators (acting on the space variable) coincide with the transition…
Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…
The explicit construction of direct and inverse Fourier's vector transform with discontinuous coefficients is presented. The technique of applying Fourier's vector transform with discontinuous coefficients for solving problems of…
The main result establishes the existence of a solution in a generalized sense for a nonlinear Dirichlet problem driven by a competing operator and exhibiting a convection term composed with an intrinsic operator. A finite dimensional…
In this article we discuss the requirements needed in order to characterise the solution space of perturbed linear integro-differential Volterra convolution equations. We highlight in general how the pointwise behaviour of perturbation…
This paper presents a direct numerical scheme to approximate the solution of all classes of nonlinear Volterra integral equations of the first kind. This computational method is based on operational matrices and vectors. The operational…
We examine two nonselfadjoint operator algebras: the weighted shift algebra, and the Volterra operator algebra. In both cases, the operator algebra is the norm closure of the polynomials in the operator norm. In the case of the weighted…
In this work we study a nonlinear Volterra equation with non-symmetric feedback that arises as a particular case of the Gurtin-MacCamy model in population dynamics. We are particularly interested in the existence of slowly oscillating…
The operator of double differentiation on a finite interval with Robin boundary conditions perturbed by the composition of a Volterra convolution operator and the differentiation one is considered. We study the inverse problem of recovering…
We give in this paper a convergence result concerning parallel asynchronous algorithm with bounded delays to solve a nonlinear fixed point problems. This result is applied to calculate the solution of a strongly monotone operator. Special…