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.
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
9.
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
10.
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
11.
The following system considered in this paper:
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