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21.
In this paper, as a first step to study the global structure of solution, we treat a class of reaction–diffusion systems with competitive interaction, and discuss a uniqueness theorem of radially symmetric solutions for the system. To do this, the comparison principle and the shooting method are employed, and the spatial profile is investigated. 相似文献
22.
Rectangular matrix solutions of the defocusing nonlinear Schrödinger equation (dNLS) are studied in quarter-plane and semi-strip. Evolution of the corresponding Weyl–Titchmarsh (Weyl) function is described in terms of the initial Weyl function and boundary conditions. In the next step, the initial Weyl function is recovered (for the quarter-plane case) from the long-time asymptotics of the wave function considered at the boundary. Thus, it is shown that the evolution of the Weyl function is uniquely defined by the boundary conditions. Moreover, a procedure to recover solutions of dNLS (uniquely defined by the boundary conditions) is given. In a somewhat different way, the same boundary value problem is also dealt with in a semi-strip (for the case of a quasi-analytic initial condition). 相似文献
23.
24.
For two types of stochastic particle systems in we show non-explosion in finite time by proving that their respective generators are L1(μ)-unique, where μ is their respective invariant (in these cases even symmetrizing) measure. We also prove the much harder L2(μ)-uniqueness in both models. 相似文献
25.
J. Extremera 《Journal of Functional Analysis》2003,197(1):212-227
Let G be a compact group. If the trivial representation of G is not weakly contained in the left regular representation of G on L02(G) and X is either Lp(G) for 1<p?∞ or C(G), then we show that every complete norm |·| on X that makes translations from (X,|·|) into itself continuous is equivalent to ||·||p or ||·||∞ respectively. If 1<p?∞ and every left invariant linear functional on Lp(G) is a constant multiple of the Haar integral, then we show that every complete norm |·| on Lp(G) that makes translations from (Lp(G),|·|) into itself continuous and that makes the map t?Lt from G into bounded is equivalent to ||·||p. 相似文献
26.
We prove a uniqueness theorem for two non-constant meromorphic functions sharing three values which improves a recent result of T.C. Alzahary. As a consequence of our main result we also improve a theorem of G. Brosch. 相似文献
27.
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.
28.
Uniqueness and value-sharing of entire functions 总被引:1,自引:0,他引:1
Xiao-Yu Zhang 《Journal of Mathematical Analysis and Applications》2008,343(2):938-950
In this paper, we study the uniqueness problems on entire functions sharing one value with the same multiplicities. We generalize and unify some previous results of Fang and Hua [M.L. Fang, X.H. Hua, Entire functions that share one value, J. Nanjing Univ. Math. Biquarterly 13 (1) (1996) 44-48], Yang and Hua [C.C. Yang, X.H. Hua, Uniqueness and value-sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math. 22 (2) (1997) 395-406] and Fang [M.L. Fang, Uniqueness and value-sharing of entire functions, Comput. Math. Appl. 44 (2002) 828-831]. 相似文献
29.
The present paper is concerned with the problem of weighted best simultaneous approximations in Banach spaces. The weighted best simultaneous approximations to sequences from S- and BS-suns in the Banach space are characterized in view of the Kolmogorov conditions. Applications are provided for weighted best simultaneous approximations from RS-sets and strict RS-sets. Our results obtained in the present paper extend and improve all earlier known results in this direction. 相似文献
30.