Global existence and uniqueness of positive solutions and optimal control for a novel model of pest control

In the present paper, a novel model of pest control governed by coupled sets of partial and ordinary differential equations is investigated in detail. Global existence and uniqueness of positive solutions to the above model are obtained. Also, the existence of optimal control is proved, and the first-order and second-order optimality conditions satisfied by optimal control are verified. In particular, the optimal control is demonstrated to be of Bang-Bang form.     

Almost periodic cellular neural networks with neutral-type proportional delays

This paper presents a new result on the existence, uniqueness and generalised exponential stability of almost periodic solutions for cellular neural networks with neutral-type proportional delays and D operator. Based on some novel differential inequality techniques, a testable condition is derived to ensure that all the state trajectories of the system converge to an almost periodic solution with a positive exponential convergence rate. The effectiveness of the obtained result is illustrated by a numerical example.     

On the existence and uniqueness of solutions in adaptive controlsystems

The issue of existence and uniqueness of solutions, which arises in the analysis of adaptive control systems, is investigated. Sufficient conditions that guarantee existence and uniqueness in positive time of solutions to differential equations describing a wide class of adaptive schemes are given. The concept of Filippov's solution is introduced as a method of dealing with discontinuous adaptive systems     

Existence and uniqueness of monotone positive solutions for an elastic beam equation with nonlinear boundary conditions

This paper is concerned with the existence and uniqueness of monotone positive solutions for an elastic beam equation with nonlinear boundary conditions. The proof of our main results is based upon a new fixed point theorem of generalized concave operators.     

On the existence,uniqueness and topological structure of solution sets to a certain fractional differential equation

The main goal of this paper is to prove two Aronszajn type theorems for some initial value problems formulated in terms of fractional derivatives. Moreover, we are going to establish a theorem on the existence and uniqueness of positive solutions.     

Anti-periodic boundary value problems of second order impulsive differential equations

This paper discusses anti-periodic boundary value problems of second order impulsive differential equations. By using the method of upper and lower solutions coupled with the monotone iterative technique, new existence results of coupled solutions and uniqueness of problems are obtained.     

Existence and uniqueness of mild solutions for abstract delay fractional differential equations

In this paper, by means of solution operator approach and contraction mapping theorem, the existence and uniqueness of mild solutions for a class of abstract delay fractional differential equations are obtained.     

Weighted pseudo-almost automorphic solutions of high-order Hopfield neural networks with neutral distributed delays

In this paper, a class of high-order Hopfield neural networks with neutral distributed delays is considered. Some sufficient conditions are obtained for the existence, uniqueness and global exponential stability of weighted pseudo-almost automorphic solutions for this class of networks by employing the Banach fixed-point theorem and differential inequality techniques. The results of this paper are completely new. An example is given to show the effectiveness of the proposed method and results.

     

Stability of Neutral Impulsive Nonlinear Stochastic Evolution Equations with Time Varying Delays

In this paper, we consider the stability of mild solutions to neutral impulsive nonlinear stochastic evolution equations with time varying delays. With the non‐Lipschitz condition, the Lipschitz condition being taken as a special case, on the impulsive term, the existence, uniqueness and sufficient conditions for the exponential stability in the pth moment and the almost sure exponential stability of the mild solutions are derived by employing a fixed point approach. An example is provided to illustrate the efficiency of the obtained theorems.     

On solution concepts and well-posedness of linear relay systems

In this paper we study the well-posedness (existence and uniqueness of solutions) of linear relay systems with respect to two different solution concepts, Filippov solutions and forward solutions. We derive necessary and sufficient conditions for well-posedness in the sense of Filippov of linear systems of relative degree one and two in closed loop with relay feedback. To be precise, uniqueness of Filippov (and also forward) solutions follows in this case if the first non-zero Markov parameter is positive. By means of an example it is shown that this intuitively clear condition is not true for systems with relative degree larger than two. The influence of the Zeno phenomenon (an infinite number of relay switching times in a finite length time interval) on well-posedness is highlighted and although linear relay systems form a rather limited subclass of hybrid dynamical systems, the consequences of the presence of the Zeno behaviour is typical for many other classes of non-smooth and hybrid systems.     

On the existence of weak solutions of nonlinear degenerate parabolic system with variable exponents

The main goal of the present paper is establishing the existence and uniqueness of weak solutions for the nonlinear degenerate reaction–diffusion system with variable exponents. A model also is proposed to characterize the invasion of cancer cells towards healthy cells with acidification environment. Moreover, the main results of this paper are obtained using regularization problem, the Faedo–Galerkin approximation method, some apriori estimates, compactness results and the Gronwall Lemma.     

Blow-up time estimates and simultaneous blow-up of solutions in nonlinear diffusion problems

This paper deals with some homogeneous Dirichlet problems of nonlinear diffusion equations. After demonstrating the existence and uniqueness of weak solutions, we prove the existence and non-existence of global solutions. The influence of coefficients and geometry of domain is shown clearly on the existence of global solutions. We give the complete classification of simultaneous blow-up of solutions with blow-up rates as well in one-dimensional space. Moreover, the bounds of blow-up time are studied for all dimensions of space domain.     

Differential periodic Riccati equations: Existence and uniqueness of nonnegative definite solutions

In this paper we consider the differential periodic Riccati equation. All the periodic nonnegative definite solutions are characterized in the more general case, providing a method for constructing them. The method is obtained from the study of the invariant subspaces of the monodromy matrix of the associated Hamiltonian system, and from the relations between these invariant subspaces and the controllability and unobservability subspaces. Finally, the method is applied to obtain necessary and sufficient conditions for the existence of any periodic nonnegative definite solution and to study the existence and uniqueness of minimal, maximal, stabilizing, and strong solutions.This work has been partially supported by Spanish DGICYT Grant No. PB91-O535.     

Global weak solutions to a spatio-temporal fractional Landau–Lifshitz–Bloch equation

The present paper deals with global existence of weak solutions of a time-space fractional Landau–Lifshitz–Bloch equation involving the weak Caputo derivative and a fractional Laplacian. We use Faedo–Galerkin method with some commutator estimates in order to prove global existence of weak solutions for the model. The uniqueness is also discussed in a special one dimensional case.     

需求依赖库存且有时变短缺拖后率的非立即变质物品库存模型

研究了时变短缺部分拖后条件下非立即变质性物品的库存补给模型,其中物品的变质率随时间变化而变化。当库存水平为正值时,市场需求受销售价格影响;当库存为负值时,不能满足的需求被部分拖后,拖后率与在缺货期间已经发生的缺货量有关。通过考虑短缺拖后率和变质率同时随时间变化对库存补给策略的影响,建立具有短缺量部分拖后的非立即变质性物品的库存模型,并且给出模型最优解存在的必要条件,得到一类更加符合实际情形的库存模型。最后,用数值算例说明模型的实际应用。     

Toward the existence and uniqueness of solutions of second-order fuzzy differential equations

In this paper the existence and uniqueness of solutions for second-order fuzzy differential equations with initial conditions under generalized H-differentiability is proved. To this end, the concept of second-order generalized differential equation is defined, which is based on an enlargement of the class of differentiable fuzzy mappings.     

Existence,Uniqueness and Stability of Mild Solutions to a Stochastic Nonlocal Delayed Reaction–Diffusion Equation

Neural Processing Letters - The aim of this paper is to investigate the existence, uniqueness and stability of mild solutions to a stochastic delayed reaction–diffusion equation with spatial...     

On the existence,uniqueness and nature of Carathéodory and Filippov solutions for bimodal piecewise affine dynamical systems

In this paper, we deal with the well-posedness (in the sense of existence and uniqueness of solutions) and nature of solutions for discontinuous bimodal piecewise affine systems in a differential inclusion setting. First, we show that the conditions guaranteeing uniqueness of Filippov solutions in the context of general differential inclusions are quite restrictive when applied to bimodal piecewise affine systems. Later, we present a set of necessary and sufficient conditions for uniqueness of Filippov solutions for bimodal piecewise affine systems. We also study the so-called Zeno behavior (possibility of infinitely many switchings within a finite time interval) for Filippov solutions.     

Algebraic Riccati equation and symplectic algebra

Questions of existence, uniqueness and the parametric dependence of solutions of the algebraic Riccati equation are considered. The different criteria for the solubility of this equation are obtained with the help of symplectic algebra.