Decay rates of Volterra equations on ℝN
This note is concerned with the linear Volterra equation of hyperbolic type on the whole space ℝN. New results concerning the decay of the associated energy as time goes to infinity were established.
Existence and asymptotic behavior of solutions for weighted -Laplacian integrodifferential system multipoint and integral boundary value problems in half line.
Existence and Asymptotic Stability of Solutions of a Perturbed Quadratic Fractional Integral Equation
Mathematics Subject Classification: 45G10, 45M99, 47H09We study the solvability of a perturbed quadratic integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions which are defined, bounded and continuous on an unbounded interval. Moreover, we will obtain some asymptotic characterization of solutions. Finally, we give an example to illustrate our abstract results.
Existence and upper semicontinuity of global attractors for neural fields in an unbounded domain.
Inequalities of solutions of Volterra integral and differential equations.
Lp decay estimates for weighted oscillatory integral operators on R.
In this paper, we formulate necessary conditions for decay rates of Lp operator norms of weighted oscillatory integral operators R and give sharp L2 estimates and nearly sharp Lp estimates.
Nonmonotone nonconvolution functions of positive type and applications
We present two sufficient conditions for nonconvolution kernels to be of positive type. We apply the results to obtain stability for one-dimensional models of chemically reacting viscoelastic materials.
On solutions of a Volterra integral equation with deviating arguments.
On the Boundedness and the Asymptotic Behaviour of the Non-Negative Solutions of Volterra-Hammerstein Integral Equations.
On the non-exponential decay to equilibrium of solutions of nonlinear scalar Volterra integro-differential equations.
On the oscillatory properties of the solutions of a class of integro- differential equations of neutral type.
On the pseudospectra of multidimensional integral operators with homogeneous kernels of degree .
On the stability of Runge-Kutta methods for delay integral equations.
On the Tjon-Wu representation of the Boltzmann equation
On the -conditional asymptotic stability of the solutions of a nonlinear Volterra integro-differential system.
On three problems of neutron transport theory
In this paper, the initial-value problem, the problem of asymptotic time behaviour of its solution and the problem of criticality are studied in the case of linear Boltzmann equation for both finite and infinite media. Space of functions where these problems are solved is chosen in such a vay that the range of physical situations considered may be so wide as possible. As mathematical apparatus the theory of positive bounded operators and of semigroups are applied. Main results are summarized in...
Oscillation of Volterra integral equations and forced functional differential equations.
Periodic and asymptotically periodic solutions of neutral integral equations.
Periodic solutions of Volterra integral equations.
Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies
Resistance to chemotherapies, particularly to anticancer treatments, is an increasing medical concern. Among the many mechanisms at work in cancers, one of the most important is the selection of tumor cells expressing resistance genes or phenotypes. Motivated by the theory of mutation-selection in adaptive evolution, we propose a model based on a continuous variable that represents the expression level of a resistance gene (or genes, yielding a phenotype) influencing in healthy and tumor cells birth/death...