共查询到20条相似文献,搜索用时 31 毫秒
1.
We use the barrier strip method to prove sufficient conditions for the global solvability of the initial value problem f(t, x, x′) = 0, x(0) = A, including the case in which the function (t, x, y) → f(t, x, y) has a singularity at x = A. 相似文献
2.
P. S. Kelevedjiev D. O’Regan N. Popivanov R. P. Agarwal 《Aequationes Mathematicae》2010,79(3):281-291
Using barrier strip type arguments we investigate the existence of solutions of the boundary value problem ${x''=f(t,x),\;t\in(0,1),\;x(0)=A,\;x'(1)=0,}Using barrier strip type arguments we investigate the existence of solutions of the boundary value problem x"=f(t,x), t ? (0,1), x(0)=A, x¢(1)=0,{x'=f(t,x),\;t\in(0,1),\;x(0)=A,\;x'(1)=0,} where the scalar function f(t, x) may be singular at x = A. 相似文献
3.
In this paper, we prove that the second order differential equation d^2x/dt^2+x^2n_1f(x)+p(t)=0with p(t + 1) = p(t), f(x + T) = f(x) smooth and f(x) 〉 0, possesses Lagrangian stability despite of the fact that the monotone twist condition is violated. 相似文献
4.
J. Brzdek 《Aequationes Mathematicae》2000,59(3):248-254
Summary. Let \Bbb K {\Bbb K} be either the field of reals or the field of complex numbers, X be an F-space (i.e. a Fréchet space) over \Bbb K {\Bbb K} n be a positive integer, and f : X ? \Bbb K f : X \to {\Bbb K} be a solution of the functional equation¶¶f(x + f(x)n y) = f(x) f(y) f(x + f(x)^n y) = f(x) f(y) .¶We prove that, if there is a real positive a such that the set { x ? X : |f(x)| ? (0, a)} \{ x \in X : |f(x)| \in (0, a)\} contains a subset of second category and with the Baire property, then f is continuous or { x ? X : |f(x)| ? (0, a)} \{ x \in X : |f(x)| \in (0, a)\} for every x ? X x \in X . As a consequence of this we obtain the following fact: Every Baire measurable solution f : X ? \Bbb K f : X \to {\Bbb K} of the equation is continuous or equal zero almost everywhere (i.e., there is a first category set A ì X A \subset X with f(X \A) = { 0 }) f(X \backslash A) = \{ 0 \}) . 相似文献
5.
R. Lucchetti P. Shunmugaraj Y. Sonntag 《Numerical Functional Analysis & Optimization》2013,34(1-2):103-115
Given a continuous function f: X→R, sufficient conditions are offered for the continuity of the value function v(A):=inf{f{x): x ε A} and of the level set multifunction Lev(A, α) := {x ε A: f(x)?α}, with respect to recently defined topologies on the closed sets of a metric space. 相似文献
6.
Patrick S. Hagan 《Studies in Applied Mathematics》1981,64(1):57-88
We consider the class of equations ut=f(uxx, ux, u) under the restriction that for all a,b,c. We first consider this equation over the unbounded domain ? ∞ < x < + ∞, and we show that very nearly every bounded nonmonotonic solution of the form u(t, x)=?(x?ct) is unstable to all nonnegative and all nonpositive perturbations. We then extend these results to nonmonotonic plane wave solutions u(t, x, y)=?(x?ct) of ut = F(uxx, uxy, ux, uy, u). Finally, we consider the class of equations ut=f(uxx, ux, u) over the bounded domain 0 < x < 1 with the boundary conditions u(t, x)=A at x=0 and u(t, x)=B at x=1, and we find the stability of all steady solutions u(t, x)=?(x). 相似文献
7.
For linear multistep methods with constant stepsize we consider error bounds in terms of weightedL
2-norms ofh
px(p) rather than ofh
px(p+1). The bounds apply to stiff systemsx'=Ax+f(t,x) where the spectrum ofA lies in a sector andf is of moderate size. 相似文献
8.
G. Zamani Eskandani Pasc Gavruta John M. Rassias Ramazan Zarghami 《Mediterranean Journal of Mathematics》2011,8(3):331-348
In this paper, we establish the general solution and investigate the generalized Hyers-Ulam stability of the following mixed
additive and quadratic functional equation
f(lx + y) + f(lx - y) = f(x + y) + f(x - y) + (l- 1)[(l+2)f(x) + lf(-x)],f(\lambda x + y) + f(\lambda x - y) = f(x + y) + f(x - y) + (\lambda - 1)[(\lambda +2)f(x) + \lambda f(-x)], 相似文献
9.
In this paper, we study the approximate controllability with preassigned responses of the nonlinear delay systems x(t)=A(t)x(t)+f(t, x(t), x((t)), u(t)) and L(x(t), x(t))=A(t)x(t)+f(t, x(t), x((t)), u(t)). The controllability is not governed by an associated linear system, but by conditions on f or A involving the domain of A(t). No compactness assumptions are imposed in the main results. 相似文献
10.
Frank Uhlig 《Numerical Algorithms》2009,52(3):335-353
We use methods of geometric computing combined with hermitean matrix eigenvalue/eigenvector evaluations to find the numerical
radius w(A) of a real or complex square matrix A simply, quickly, and accurately. The numerical radius w(A) is defined as the maximal distance of points in the field of values F(A) = { x* A x | ||x||2 = 1 }F(A) = \{ x^* A x \mid \|x\|_2 = 1 \} from zero in ℂ. Its value is an indicator of the transient behavior of the discrete dynamical system f
k + 1 = Af
k
. We describe and test a MATLAB code for solving this optimization problem that can have multiple and even infinitely many
solutions with maximal distance. 相似文献
11.
Another logarithmic functional equation 总被引:1,自引:0,他引:1
K. J. Heuvers 《Aequationes Mathematicae》1999,58(3):260-264
Summary. Let f : ]0,¥[? \Bbb R f :\,]0,\infty[\to \Bbb R be a real valued function on the set of positive reals. The functional equations¶¶f(x + y) - f(x) - f(y) = f(x-1 + y-1) f(x + y) - f(x) - f(y) = f(x^{-1} + y^{-1}) ¶and¶f(xy) = f(x) + f(y) f(xy) = f(x) + f(y) ¶are equivalent to each other. 相似文献
12.
The following system considered in this paper:
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