Uniqueness and existence for perturbed focal boundary value problems

Assuming a uniqueness assumption on the variational boundary value problems, uniqueness and existence is established for problems which generalize focal boundary value problems.     

On the uniqueness of optimal solutions in continuous location theory

This paper deals with the uniqueness of an optimal solution in general continuous single facility minisum and minimax location problems. We define the concept of an S-norm and obtain general conditions which guarantee the existence of a unique optimal location. Some consequences for the uniqueness of optimal locations in multi-facility location problems are discussed.     

Uniqueness for nonlinear degenerate problems

We prove existence and uniqueness results for weak solutions of nonlinear degenerate problems arising in various physical models. The main novelty in the article concerns the uniqueness, which employs a technique based in showing that weak solutions are also entropy solutions, for which uniqueness follows from a straightforward adaptation of known results. We treat equations with lower order terms that have a particular structure and show with a counterexample that for general lower order terms the uniqueness does not hold.AMS Subject Classification: 35D99, 35K65, 35R35.     

Uniqueness of multiple Walsh series for the convergence on binary cubes

We consider uniqueness problems for multiple Walsh series convergent on binary cubes on a multidimensional binary group. We find conditions under which a given finite or countable set is a set of uniqueness.     

共享三个值的亚纯函数的唯一性问题

This paper investigate the uniqueness problems for meromorphic functions that share three values CM and proves a uniqueness theorem on this topic which can be used to improve some previous related results.     

Uniqueness and counterexamples in some inverse source problems

Uniqueness of a solution is investigated for some inverse source problems arising in linear parabolic equations. We prove new uniqueness results formulated in Theorems 3.1 and 3.2. We also show optimality of the conditions under which uniqueness holds by explicitly constructing counterexamples, that is by constructing more than one solution in the case when the conditions for uniqueness are violated.     

ON ALMOST PERIODIC SOLUTIONS OF AHIGHER ORDER ALMOST PERIODIC SYSTEM

1IntroductionConsiderthel'Ollowingdifferentialequationdx~~A(.t)x g(t,x),(l)dt.wherexeR",t6R,A(t)=(a,,(t)),,..istillnxncontinlloust'llllctiollmatrixinR,g(t,x)isanat-dimensionalcolltinuousfunctionvectorinRxR".Thepaper[l,21dealedwil;htheproblemontheexistence…     

非线性解耦问题的解及其唯一性

一、引言控制系统的反馈解耦问题已有很多研究,对于非线性系统,最先开始的研究是文[1]和[2].它们推广了单对单解耦问题著名的 Falb-Wolovich 条件.具有开拓性的研究是文[3]和[4].在获奖文[4]中,Isidori 等首次给出了非线性解耦问题的几何刻划.之后有更多、更进一步的研究.关于解耦问题的历史和发展,请读者参阅文献[8]和[9].近年来,解耦问题的研究兴趣还包括有动态反馈和奇异反馈设计.     

Duality and uniqueness of convex solutions to stationary Hamilton-Jacobi equations

Value functions for convex optimal control problems on infinite time intervals are studied in the framework of duality. Hamilton-Jacobi characterizations and the conjugacy of primal and dual value functions are of main interest. Close ties between the uniqueness of convex solutions to a Hamilton-Jacobi equation, the uniqueness of such solutions to a dual Hamilton-Jacobi equation, and the conjugacy of primal and dual value functions are displayed. Simultaneous approximation of primal and dual infinite horizon problems with a pair of dual problems on finite horizon, for which the value functions are conjugate, leads to sufficient conditions on the conjugacy of the infinite time horizon value functions. Consequently, uniqueness results for the Hamilton-Jacobi equation are established. Little regularity is assumed on the cost functions in the control problems, correspondingly, the Hamiltonians need not display any strict convexity and may have several saddle points.

     

A uniqueness criterion for linear problems of wave-body interaction

The question of uniqueness for linearized problems describinginteraction of submerged bodies with an ideal unbounded fluidis far from its final resolution. In this work a new criterionof uniqueness is suggested based on Green's integral identityand maximum principles for elliptic differential equations.The criterion is formulated as an inequality involving integralsof the Green function over the bodies' wetted surfaces. Thiscriterion is quite general and applicable for any number ofsubmerged bodies of arbitrary shape (provided the boundary issufficiently regular) and in any dimension; it can also be generalizedto more complicated elliptic problems. Very simple bounds arealso derived from the criterion, which deliver uniqueness setsin the space of parameters defined by submergence of the systemof bodies and the frequency of oscillation. Results of numericalinvestigation and comparison with known uniqueness criteriaare presented.     

一类泛函微分方程的周期解的存在性、唯一性及全局吸引性

该文研究了一类具有分布滞量的微分系统的周期解的存在性、唯一性及全局吸引性等问题.利用不动点方法和Lyapunov泛函方法,建立了保证该类系统周期解的存在性、唯一性、一致稳定性及全局吸引性的充分条件.     

THE EXISTENCE, UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTION FOR A CLASS OF NONLINEAR SYSTEM

In this paper, we study the problems on the existence, uniqueness and stability of almost periodic solution for a class of nonlinear system. Using fixed point theorem and Lyapunov functional, the sufficient conditions are given which guarantee the existence, uniqueness and stability of almost periodic solution for the system.     

Generic well-posedness of nonconvex optimal control problems

The Tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrands f which satisfy convexity and growth conditions. In our previous work a generic existence and uniqueness result (with respect to variations of the integrand of the integral functional) without the convexity condition was established for a class of optimal control problems satisfying the Cesari growth condition. In this paper we extend this generic existence and uniqueness result to a class of optimal control problems in which the right-hand side of differential equations is also subject to variations.     

THE EXISTENCE AND UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTIONS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS

ＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＡＮＤＳＴＡＢＩＬＩＴＹＯＦＡＬＭＯＳＴＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＦＯＲＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＩＮＦＩＮＩＴＥＤＥＬＡＹＳＷＡＮＧＱＵＡＮＨＮＹ...     

一类混合似变分不等式问题解的存在唯一性

本文中,我们首先给出了一类混合似变分不等式问题．接着,在Banach空间中研究了它的解的存在性和唯一性．最后,讨论了混合似变分不等式问题的扰动问题,并证明了扰动问题的解的存在唯一性定理．     

Uniqueness for inverse problems of determining orders of multi-term time-fractional derivatives of diffusion equation

This article proves the uniqueness for two kinds of inverse problems of identifying fractional orders in diffusion equations with multiple time-fractional derivatives by pointwise observation. By means of eigenfunction expansion and Laplace transform, we reduce the uniqueness for our inverse problems to the uniqueness of expansions of some special function and complete the proof.     

One-phase inverse Stefan problems with unknown nonlinear sources

We consider quasilinear models of inverse problems with phase transitions in a domain whose external boundary is a phase front with an unknown dependence on time. Additional information for finding the sources is given in the form of final overdetermination for the solution of the direct Stefan problem. On the basis of the duality principle, we obtain sufficient conditions for the uniqueness of the solution in Hölder classes for the considered inverse Stefan problems. We present examples in which the uniqueness property is lost when extending the set of admissible solutions.     

A class of free boundary problems to quasi-linear parabolic equations

1.IntroductionStefan-likeproblemswithakineticconditiononthefreeboundarytolinearparabolicequationshavebeenconsideredbyseveralauthors(see[1-4]andreferencestherein),buttoquasi-linearonesproblemssimilar,whichareconsideredhereandmoredifficultthanpreviouso...     

On Generic Existence and Uniqueness in Nonconvex Optimal Control Problems

We derive conditions for generic existence and uniqueness of optimal control and trajectories for some class of finite-dimensional optimal control problems in the absence of traditional convexity assumptions. It is shown that for these problems existence and uniqueness of optimal control for a given initial point x is equivalent to the differentiability of optimal value functions at x. These results are obtained in the general framework of representation formulas for (sub-)gradients of inf-envelope functions which appear in nonsmooth analysis.     

Inverse problem on a tree-shaped network: unified approach for uniqueness

In this article, we prove uniqueness results for coefficient inverse problems regarding wave, heat or Schrödinger equation on a tree-shaped network, as well as the corresponding stability result of the inverse problem for the wave equation. The objective is the determination of the potential on each edge of the network from the additional measurement of the solution at all but one external end points. Several results have already been obtained in this precise setting or in similar cases, and our main goal is to propose a unified and simpler method of proof of some of these results. The idea which we will develop for proving the uniqueness is to use a more traditional approach in coefficient inverse problems by Carleman estimates. Afterwards, using an observability estimate on the whole network, we apply a compactness–uniqueness argument and prove the stability for the wave inverse problem.