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1.
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. 相似文献
2.
《Nonlinear Analysis: Theory, Methods & Applications》2010,72(12):6109-6115
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. 相似文献
3.
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. 相似文献
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D. D. Hai 《Proceedings of the American Mathematical Society》2005,133(1):223-228
We obtain necessary and sufficient conditions for the existence of positive solutions for a class of sublinear Dirichlet quasilinear elliptic systems.
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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. 相似文献
6.
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. 相似文献
7.
Zengji Du 《Applied mathematics and computation》2011,218(7):2981-2987
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. 相似文献
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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. 相似文献
11.
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)=
eau. 相似文献
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13.
Hideo Deguchi 《Monatshefte für Mathematik》2009,156(3):211-231
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.
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Zhijun Zhang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(16):5544-5553
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 RN, 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]. 相似文献
17.
In this paper, sufficient conditions are obtained for the existence of a unique periodic solution for a class of differential systems. 相似文献
18.
EXISTENCE AND UNIQUENESS FOR SECOND-ORDER VECTOR BOUNDARY VALUE PROBLEM OF NONLINEAR SYSTEMS 总被引:1,自引:0,他引:1
Du Zengji Lin Xiaojie Ge Weigao 《高校应用数学学报(英文版)》2005,20(3):323-330
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. 相似文献
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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. 相似文献