Existence,uniqueness and continuous dependence for hereditary systems

Summary An hereditary system is a system whose present state is determined in some way by its past history. We formulate a class of such systems which includes functional differential equations of retarded type and many equations of neulral type as well as Volterra integral equations. Theorems of existence, uniqueness, continuation and continuous dependence are proved. Preparation of this paper was sponsored in part by the Office of Naval Research under Contract NONR 233(76). Reproduction in whole or in part is permitted for any purpose of the United States Government. Entrata in Redazione il 22 gennaio 1969.     

Existence and uniqueness of solutions of piecewise nonlinear systems

In this paper, we consider the existence and the uniqueness of solutions of piecewise nonlinear systems. We will present some necessary and sufficient conditions for the existence and the uniqueness of solutions of this class of systems.     

Existence and uniqueness of solutions of piecewise nonlinear systems

In this paper, we consider the existence and the uniqueness of solutions of piecewise nonlinear systems. We will present some necessary and sufficient conditions for the existence and the uniqueness of solutions of this class of systems.     

Existence and uniqueness of solutions for quasilinear elliptic systems

We obtain necessary and sufficient conditions for the existence of positive solutions for a class of sublinear Dirichlet quasilinear elliptic systems.

     

Existence,uniqueness and stability results of random impulsive semilinear differential systems

In this paper, we consider semilinear differential systems with random impulses. We study the existence and uniqueness of the solutions by relaxing the linear growth conditions, sufficient conditions for stability through continuous dependence on initial conditions and the exponential stability of this system have been established.     

Existence,uniqueness and stability of pyramidal traveling fronts in reaction-diffusion systems

In the one-dimensional space, traveling wave solutions of parabolic differential equations have been widely studied and well characterized. Recently, the mathematical study on higher-dimensional traveling fronts has attracted a lot of attention and many new types of nonplanar traveling waves have been observed for scalar reaction-diffusion equations with various nonlinearities. In this paper, by using the comparison argument and constructing appropriate super- and subsolutions, we study the existence, uniqueness and stability of threedimensional traveling fronts of pyramidal shape for monotone bistable systems of reaction-diffusion equations in R³. The pyramidal traveling fronts are characterized as either a combination of planar traveling fronts on the lateral surfaces or a combination of two-dimensional V-form waves on the edges of the pyramid. In particular, our results are applicable to some important models in biology, such as Lotka-Volterra competition-diffusion systems with or without spatio-temporal delays, and reaction-diffusion systems of multiple obligate mutualists.     

Existence and uniqueness results for third-order nonlinear differential systems

Sufficient conditions are given for the existence of solutions to third order boundary value problems for nonlinear differential systems. Some appropriate conditions are given to guarantee that the Nagumo condition is satisfied. By constructing appropriate a lower solution-upper solution pair, a concept that is defined in this paper, the uniqueness result of the problem is also established. The emphasis here is that the differential systems has nonlinear dependence on all over order derivatives and the boundary conditions are nonlinear.     

Impulse systems with fixed shock times of general disposition: Existence,uniqueness of solution,and the well-posedness of the Cauchy problem

One investigates systems of differential equations with impulse actions at fixed times, when the sequence of the shock times may have finite limit points. For such systems one obtains theorems for the existence and uniqueness of the solution, as well as for the well-posedness of the Cauchy problem.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 2, pp. 230–237, February, 1990.     

Existence and uniqueness results for large solutions of general nonlinear elliptic equations

We study under what condition there exists a solution of -u+f(u)=0 in a domain which blows-up on the boundary, independently of the regularity of the boundary, and we provide criteria for uniqueness. We apply our results to the case f(u)= e^au.     

Existence,uniqueness and stability of weak solutions of parabolic systems with discontinuous nonlinearities

This paper is devoted to the study of the initial value problem for parabolic systems with discontinuous nonlinearities from the viewpoint of the existence, uniqueness and stability of weak solutions. Also the relationship with the solutions of the corresponding differential inclusions is studied.      

概周期系统概周期解的存在唯一性

运用Ｌｉａｐｕｎｏｖ函数，研究了概周期系统概周期解的存在唯一性，得到了一个方便应用的判定定理．     

Positive solutions of Lane-Emden systems with negative exponents: Existence, boundary behavior and uniqueness

We study the existence, boundary behavior and uniqueness of solutions for the singular elliptic system −Δu=u^−pv^−q,−Δv=u^−rv^−s,u>0,v>0,x∈Ω,u|_∂Ω=v|_∂Ω=0, where Ω is a bounded domain with smooth boundary in R^N, p,s≥0 and q,r>0. Our results are obtained in a range of p,q,r,s different from those in [M. Ghergu, Lane-Emden systems with negative exponents, J. Funct. Anal. 258 (2010) 3295-3318].     

Existence and uniqueness of periodic solution for a class of differential systems

In this paper, sufficient conditions are obtained for the existence of a unique periodic solution for a class of differential systems.     

EXISTENCE AND UNIQUENESS FOR SECOND-ORDER VECTOR BOUNDARY VALUE PROBLEM OF NONLINEAR SYSTEMS

This paper is concerned with the following second-order vector boundary value problem ：x^R=f（t,Sx,x,x＇）,0〈t〈1,x（0）=A,g（x（1）,x＇（1））=B,where x,f,g,A and B are n-vectors. Under appropriate assumptions,existence and uniqueness of solutions are obtained by using upper and lower solutions method.     

Existence,uniqueness, and stability of nonlinear evolution equations

In this paper we study existence, uniqueness, and stability of nonlinear evolution equations. We develop a new type of perturbation result for a C₀ semigroup in Banach space, where the nonlinear operators are not necessarily m-accretive or everywhere defined. Assuming that the semigroup has a smoothing property we obtain local existence, uniqueness and regularity results. We then establish a Liapunov theory which enables us to examine stability. To illustrate our theory several simple examples are presented.