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101.
We introduce nonlocal flows that commute with those of the classical Toda hierarchy. We define a logarithm of the difference Lax operator and use it to obtain a Lax representation of the new flows.  相似文献   
102.
We consider some initial-boundary value problems for the linear and nonlinear heat equation where the gradient of the solution is prescribed on the boundary. Assuming that a solution exists, we obtain bounds for the solution and its gradient by maximum principle arguments or by means of differential and integral inequalities.  相似文献   
103.
In this paper, we shall establish sufficient conditions for the existence of integral solutions for some nondensely defined evolution impulsive differential inclusions in Banach spaces with nonlocal conditions.  相似文献   
104.
We generalize a previous result of Ikehata (Math. Methods Appl. Sci., in press), which studies the critical exponent problem of a semilinear damped wave equation in the one-dimensional half space, to the general N-dimensional half space case. That is to say, one can show the small data global existence of solutions of a mixed problem for the equation uttΔu+ut=|u|p with the power p satisfying p∗(N)=1+2/(N+1)<p?N/[N−2]+ if we deal with the problem in the N-dimensional half space.  相似文献   
105.
For the quantum integer [n]q=1+q+q2+?+qn−1 there is a natural polynomial multiplication such that [m]qq[n]q=[mn]q. This multiplication leads to the functional equation fm(q)fn(qm)=fmn(q), defined on a given sequence of polynomials. This paper contains various results concerning the construction and classification of polynomial sequences that satisfy the functional equation, as well open problems that arise from the functional equation.  相似文献   
106.
This paper considers the following Cauchy problem for semilinear wave equations in $n$ space dimensions $$\align \square\p &=F(\partial\p ),\\p (0,x)&=f(x),\quad \partial_t\p (0,x)=g(x), \endalign$$ where $\square =\partial_t^2-\triangle$ is the wave operator, $F$ is quadratic in $\partial\p$ with $\partial =(\partial_t,\partial_{x_1},\cdots ,\partial_{x_n})$. The minimal value of $s$ is determined such that the above Cauchy problem is locally well-posed in $H^s$. It turns out that for the general equation $s$ must satisfy $$s>\max\Big(\frac{n}{2}, \frac{n+5}{4}\Big).$$ This is due to Ponce and Sideris (when $n=3$) and Tataru (when $n\ge 5$). The purpose of this paper is to supplement with a proof in the case $n=2,4$.  相似文献   
107.
We present new oscillation criteria for the second order nonlinear neutral delay differential equation [y(t)-py(t-τ)]'+ q(t)y λ (g(t)) sgn y(g(t)) = 0, tt 0. Our results solve an open problem posed by James S.W . Wong [24]. The relevance of our results becomes clear due to a carefully selected example. This revised version was published online in June 2006 with corrections to the Cover Date.  相似文献   
108.
We construct a new family of cyclic difference sets with parameters ((3 d – 1)/2, (3 d – 1 – 1)/2, (3 d – 2 – 1)/2) for each odd d. The difference sets are constructed with certain maps that form Jacobi sums. These new difference sets are similar to Maschietti's hyperoval difference sets, of the Segre type, in characteristic two. We conclude by calculating the 3-ranks of the new difference sets.  相似文献   
109.
By means of a Carleman estimate, we obtain several observability inequalities by internal observation for hyperbolic equations with lower-order terms. Also, we apply our observability results to an exact controllability problem and an inverse wave source problem.  相似文献   
110.
An Epidemic Model with a Time Delay in Transmission   总被引:1,自引:0,他引:1  
We study a mathematical model which was originally suggested by Greenhalgh and Das and takes into account the delay in the recruitment of infected persons. The stability of the equilibria are also discussed. In addition, we show that the introduction of a time delay in the transmission term can destabilize the system and periodic solutions can arise by Hopf bifurcation.  相似文献   
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