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1.
In this paper, the first order impulsive dynamic equations on time scales is considered. The existence and uniqueness of solution for a class of nonlinear impulsive dynamic equations on time scales is proved.  相似文献   

2.
The local existence and local asymptotic stability of nontrivial p-periodic solutions of p-periodically forced discrete systems are proven using Liapunov-Schmidt methods. The periodic solutions bifurcate transcritically from the trivial solution at the critical value n=ncr of the bifurcation parameter with a typical exchange of stability. If the trivial solution loses (gains) stability as n is increased through ncr , then the periodic solutions on the nontrivial bifurcating branch are locally asymptotically stable if and only if they correspond to n>ncr (n ncr ).  相似文献   

3.
The existence of periodic and almost periodic solutions of nonlinear discrete Volterra equations with unbounded delay is obtained by using stability properties of a bounded solution.  相似文献   

4.
设n,a,b,c是正整数,gcd(a,b,c)=1,a,b≥3,且丢番图方程a~x+b~y=c~z只有正整数解(x,y,z)=(1,1,1).证明了若(x,y,z)是丢番图方程(an)~x+(bn)~y=(cn)~z的正整数解且(x,y,z)≠(1,1,1),则yzz或xzy.还证明了当(a,b,c)=(3,5,8),(5,8,13),(8,13,21),(13,21,34)时,丢番图方程(an)~x+(bn)~y=(cn)~z只有正整数解(x,y,z)=(1,1,1).  相似文献   

5.
Summary A natural extension of Jensen's functional equation on the real line is the equationf(xy) + f(xy –1 ) = 2f(x), wheref maps a groupG into an abelian groupH. We deduce some basic reduction formulas and relations, and use them to obtain the general solution on special groups.  相似文献   

6.
In this paper, a delayed ratio-dependent predator–prey model with monotonic functional response and impulse is investigated. By using the continuation theorem of coincidence degree theory, an easily verifiable sufficient condition for the existence of at least one positive periodic solution is established. In particular, our results generalize some known criteria.  相似文献   

7.
8.
Linear delay difference equations with variable coefficients and constant delays are considered. By the use of an appropriate solution of the so called generalized characteristic equation, an asymptotic result is obtained and a stability criterion is established.  相似文献   

9.
本文讨论了广义阿贝尔微分方程.利用不动点定理,得到了方程存在两个非零周期解的充分条件.同时,我们还讨论了不存在非零周期解和存在唯一非零周期解的情况.  相似文献   

10.
在本文中, 我们得到了Type I McKay Distribution的Stein方程的通解. 我们证明了其Stein方程的有界解存在且唯一. 进一步的我们研究了其应的有界解的一些性质. 这对用Stein方法取研究Type I McKay分布的逼近可能会有一些作用.  相似文献   

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