共查询到20条相似文献,搜索用时 93 毫秒
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本文论讨了三个问题:①二阶非线性微分方程的初值问题;②运用非线性算子证明了非平凡解的存在性和唯一性;③给出了一个非负非平凡解的估计式. 相似文献
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运用变分方法和临界点理论研究2n阶差分方程边值问题非平凡解的存在性,推广和完善了近期的一些结果. 相似文献
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一类积-微分参数方程的非负解 总被引:4,自引:1,他引:3
本文讨论了迁移理论中一类控制临界本征方程.运用L2空间上的线性算子理论,我们获得了这类方程的的控制参数在复平面的分布情况及非负解存在唯一的条件. 相似文献
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广义Lienard方程非平凡周期解的存在性 总被引:4,自引:1,他引:3
本文讨论广义Lienard方程x+f(x)ψ(x)x+g(x)η(x)=0非平凡周期解的存在性,所获结果推广并改进了一些现有的关于Lienard方程周期解的存在性定理。 相似文献
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郝兆才 《数学物理学报(A辑)》2001,21(2):225-229
该文研究了一类半线性三阶差分方程边值问题Δ3u(t)+a(t)f(u(t))=0,2≤T≤T+2,u(0)=u(1)=u(T+3)=0的非负解,得到了该方程在锥与环形域相交部分非负解的存在性,包含、改近和推广了文[3,4,5,6]的主要结果. 相似文献
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本文研究了Maxwell-Boltzmann方程非负解的极值原理以及随时间延伸而逐渐衰减的解的时间渐近行为。 相似文献
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叠合度的缺方向性与边值共振问题的非平凡解 总被引:2,自引:0,他引:2
本文在无任何附加条件的情况下证明了叠合度也具有Leray-Schauder度的缺方向性质,完全解决了前人工作中的遗留问题.作为这一结果的应用,证明了一类m-点边值问题和Duffing方程周期边值问题非平凡解的存在性结果. 相似文献
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讨论了齐次Neumann边界条件下食饵有外界常收获率的捕食-食饵模型的共存态首先分析了正常数解的稳定性以及非常数正平衡解不存在的条件.其次,基于对平衡解的先验估计,利用拓扑度理论,给出了此平衡态系统非常数正解的存在性. 相似文献
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Christoph Walker 《Journal of Differential Equations》2010,248(7):1756-1776
Existence of nontrivial nonnegative equilibrium solutions for age-structured population models with nonlinear diffusion is investigated. Introducing a parameter measuring the intensity of the fertility, global bifurcation is shown of a branch of positive equilibrium solutions emanating from the trivial equilibrium. Moreover, for the parameter-independent model we establish existence of positive equilibria by means of a fixed point theorem for conical shells. 相似文献
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《Nonlinear Analysis: Theory, Methods & Applications》2004,56(2):227-240
This paper is devoted to study the existence of nontrivial positive solution of a class of elliptic system with Dirichlet Data. By using the abstract linking theorems on product space we established in Zhao et al. (Nonlinear Anal. 49 (2002) 431) we obtain the existence of three nonnegative solutions for a class of elliptic systems and the existence of a nontrivial positive solution for the problem related to the model of competing species systems involving critical Sobolev exponents. 相似文献
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We study the structure of positive solutions to the equation ?mΔmu-um-1+f(u)=0 with homogeneous Neumann boundary condition. First, we show the existence of a mountain-pass solution and find that as ?→0+ the mountain-pass solution develops into a spike-layer solution. Second, we prove that there is an uniform upper bound independent of ? for any positive solution to our problem. We also present a Harnack-type inequality for the positive solutions. Finally, we show that if 1<m?2 holds and ? is sufficiently large, any positive solution must be a constant. 相似文献
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A periodic predator–prey-chain system with impulsive effects is considered. By using the global results of Rabinowitz and standard techniques of bifurcation theory, the existence of its trivial, semi-trivial and nontrivial positive periodic solutions is obtained. It is shown that the nontrivial positive periodic solution for such a system may be bifurcated from an unstable semi-trivial periodic solution. Furthermore, the stability of these periodic solutions is studied. 相似文献
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Zongming Guo 《偏微分方程(英文版)》2001,14(4):365-383
Structure of least-energy solutions to singularly perturbed semilinear Dirichlet problem ε²Δu - u^α + g(u) = 0 in Ω,u = 0 on ∂Ω, Ω ⊂ ⋅R^N a bounded smooth domain, is precisely studied as ε → 0^+, for 0 < α < 1 and a superlinear, subcritical nonlinearity g(u). It is shown that there are many least-energy solutions for the problem and they are spike-layer solutions. Moreover, the measure of each spike-layer is estimated as ε → 0^+ . 相似文献
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An original construction of the exact nonnegative solution of multidimensional nonlinear diffusion equations is proposed and
studied. On substituting this construction into the original equation, we obtain a system of algebro-differential equations
in which the number of equations exceeds the number of unknown functions. It is proved that the resulting system possesses
nontrivial solutions. On the basis of this result, we construct exact non-self-similar explicit nonnegative solutions anisotropic
with respect to the space variables both of the class of equations of a porous medium (nonstationary filtration) and of the
class of equations involving nonlinear thermal conductivity with negative exponent. In particular, this class contains the
so-called equations of rapid and limit diffusion.
Translated fromMatematicheskie Zametki, Vol. 67, No. 2, pp. 250–256, February, 2000. 相似文献
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本文在有界正则域内研究了一类加权拟线性抛物方程组.由单个抛物方程相关的已知结论得到此类方程组的非负entropy解的正下界,然后利用一般的Picone恒等式并构造适当的检验函数,证明此类方程组的非负entropy解不存在. 相似文献