Nonconvolution nonlinear integral Volterra equations with monotone operators

Existence of Traveling Waves of Lotka Volterra Type Models with Delayed Diffusion Term and Partial Quasimonotonicity

This paper is concerned with the existence of traveling wave solutions for diffusive two-species Lotka-Volterra systems with delay in both the reaction and diffusion terms without monotonicity. We extend the partial or cross monotone iteration method to systems that satisfy the partial quasi-monotone condition via construction appropriate upper and lower solutions. This is done by using Schauder's fixed point theorem.

弱竞争Lotka-Volterra系统中的非单调行波

Non-Monotone Traveling Waves of the Weak Competition Lotka-Volterra System

本文研究弱竞争Lotka-Volterra反应扩散系统中行波的存在性，通过构造改进的上下解和Schauder不动点定理，证明了所有波速s≥s*≥max{2,2√(ad)}下的行波存在，并给出了非单调行波出现的可验证条件。

具有完全单调核的随机Volterra积分方程与在Hilbert空间上的随机微分方程的最优控制

Optimal control of stochastic Volterra integral equations with completely monotone kernels and stochastic differential equations on Hilbert spaces with unbounded control and diffusion operators

本文研究了具有完全单调核的随机Volterra积分方程的最优控制问题，通过马尔可夫提升方法将其转化为Hilbert空间上的随机微分方程问题，并证明了新的平滑性质，从而建立了Hamilton-Jacobi-Bellman方程的弱解存在性和唯一性，以及构造了最优反馈控制。

Completely monotone functions and some classes of fractional evolution equations

The abstract Cauchy problem for the distributed order fractional evolution equation in the Caputo and in the Riemann-Liouville sense is studied for operators generating a strongly continuous one-parameter semigroup on a Banach space. Continuous as well as discrete distribution of fractional time-derivatives of order less than one are considered. The problem is reformulated as an abstract Volterra integral equation. It is proven that its kernel satisfy certain complete monotonicity properties. Based on these properties, the well-posedness of the problem is established and a series expansion of …

Traveling Wave Solutions for Lotka-Volterra System Re-Visited

Using a new method of monotone iteration of a pair of smooth lower- and upper-solutions, the traveling wave solutions of the classical Lotka-Volterra system are shown to exist for a family of wave speeds. Such constructed upper and lower solution pair enables us to derive the explicit value of the minimal (critical) wave speed as well as the asymptotic rates of the wave solutions at infinities. Furthermore, the traveling wave corresponding to each wave speed is unique modulo a translation of the origin. The stability of the traveling wave solutions with non-critical wave speed is also studied …

On a multivalued differential equation with nonlocality in time

The initial value problem for a multivalued differential equation is studied, which is governed by the sum of a monotone, hemicontinuous, coercive operator fulfilling a certain growth condition and a Volterra integral operator in time of convolution type with exponential decay. The two operators act on different Banach spaces where one is not embedded in the other. The set-valued right-hand side is measurable and satisfies certain continuity and growth conditions. Existence of a solution is shown via a generalisation of the Kakutani fixed-point theorem.