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Shuxia Pan 《Journal of Mathematical Analysis and Applications》2008,346(2):415-424
This paper is concerned with the existence of traveling wave fronts for delayed non-local diffusion systems without quasimonotonicity, which can not be answered by the known results. By using exponential order, upper-lower solutions and Schauder's fixed point theorem, we reduce the existence of monotone traveling wave fronts to the existence of upper-lower solutions without the requirement of monotonicity. To illustrate our results, we establish the existence of traveling wave fronts for two examples which are the delayed non-local diffusion version of the Nicholson's blowflies equation and the Belousov-Zhabotinskii model. These results imply that the traveling wave fronts of the delayed non-local diffusion systems without quasimonotonicity are persistent if the delay is small. 相似文献
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Noncompact convexificators, which provide upper convex and lower concave approximations for a continuous function, are defined. Various calculus rules, including extremality and mean-value properties, are presented. Regularity conditions are given for convexificators to be minimal. A characterization of quasiconvexity of a continuous function is obtained in terms of the quasimonotonicity of convexificators. 相似文献
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Reinhard John 《Mathematical Programming》2000,88(1):147-155
It is shown that pseudomonotone and quasimonotone maps can be characterized by a first order property provided they are regular.
This result extends the well known characterization of nonvanishing generalized monotone maps to an essentially larger class.
The paper supplements a recent contribution by Crouzeix and Ferland (1996) and solves a related open problem concerning homogeneous
excess demand functions which occur in general equilibrium theory.
Received: April 10, 1998 / Accepted: February 29, 2000?Published online April 20, 2000 相似文献
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The purpose of this paper is to introduce and study systems of strong implicit vector variational inequalities. Under suitable
conditions, some existence results for systems of strong implicit vector variational inequalities are established by the Kakutani--Fan--Glicksberg
fixed point theorem.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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Let A be a set, and let E be the Banach space of bounded functions : A R, equipped with its natural order. With a rectangle R = (a,b) × (0,T] let F(x,t,) : R × E E be a bounded, continuous function satisfying a local Hölder condition and being quasimonotone increasing with respect to . Then there exists a solution u: [a,b] × [0,T] E of the problem ut(x,t) – uxx(x,t) = F(x,t,u(x,t)) ((x,t) R), u(x,t) = 0 ((x,t) R R). 相似文献
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Traveling Wave Fronts of Reaction-Diffusion Systems with Delay 总被引:18,自引:0,他引:18
This paper deals with the existence of traveling wave front solutions of reaction-diffusion systems with delay. A monotone
iteration scheme is established for the corresponding wave system. If the reaction term satisfies the so-called quasimonotonicity
condition, it is shown that the iteration converges to a solution of the wave system, provided that the initial function for
the iteration is chosen to be an upper solution and is from the profile set. For systems with certain nonquasimonotone reaction
terms, a convergence result is also obtained by further restricting the initial functions of the iteration and using a non-standard
ordering of the profile set. Applications are made to the delayed Fishery–KPP equation with a nonmonotone delayed reaction
term and to the delayed system of the Belousov–Zhabotinskii reaction model.
An erratum to this article is available at . 相似文献
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本文利用Schauder不动点定理和上、下解技术,研究了高维格上时滞反应扩散方程组当非线性项满足拟单调条件、指数拟单调条件、部分拟单调条件以及部分指数拟单调条件时行波解的存在性. 相似文献