共查询到20条相似文献,搜索用时 31 毫秒
1.
Zhiting Xu 《Monatshefte für Mathematik》2009,118(4):187-199
Some necessary and sufficient conditions for nonoscillation are established for the second order nonlinear differential equation
(r(t)y(x(t))|x¢(t)|p-1x¢(t))¢+c(t)f(x(t))=0, t 3 t0,(r(t)\psi(x(t))\vert x^{\prime}(t)\vert^{p-1}x^{\prime}(t))^{\prime}+c(t)f(x(t))=0,\quad t\ge t_0, 相似文献
2.
We consider the Hill operator
Ly = - y¢¢ + v(x)y, 0 £ x £ p,Ly = - y^{\prime \prime} + v(x)y, \quad0 \leq x \leq \pi, 相似文献
3.
P. Shvartsman 《Geometric And Functional Analysis》2001,11(4):840-868
We prove a Helly-type theorem for the family of all k-dimensional affine subsets of a Hilbert space H. The result is formulated in terms of Lipschitz selections of set-valued mappings from a metric space (M,r) ({\cal M},\rho) into this family.¶Let F be such a mapping satisfying the following condition: for every subset M¢ ì M {\cal M'} \subset {\cal M} consisting of at most 2k+1 points, the restriction F|M¢ F|_{\cal M'} of F to M¢ {\cal M'} has a selection fM¢ (i.e. fM¢(x) ? F(x) for all x ? M¢) f_{\cal M'}\,({\rm i.e.}\,f_{\cal M'}(x) \in F(x)\,{\rm for\,all}\,x\,\in {\cal M'}) satisfying the Lipschitz condition ||fM¢(x) - fM¢(y)|| £ r(x,y ), x,y ? M¢ \parallel f_{\cal M'}(x) - f_{\cal M'}(y)\parallel\,\le \rho(x,y ),\,x,y \in {\cal M'} . Then F has a Lipschitz selection f : M ? H f : {\cal M} \to H such that ||f(x) - f(y) || £ gr(x,y ), x,y ? M \parallel f(x) - f(y) \parallel\,\le \gamma \rho (x,y ),\,x,y \in {\cal M} where g = g(k) \gamma = \gamma(k) is a constant depending only on k. (The upper bound of the number of points in M¢ {\cal M'} , 2k+1, is sharp.)¶The proof is based on a geometrical construction which allows us to reduce the problem to an extension property of Lipschitz mappings defined on subsets of metric trees. 相似文献
4.
Harald Woracek 《Monatshefte für Mathematik》2012,33(3):105-149
A string is a pair (L, \mathfrakm){(L, \mathfrak{m})} where L ? [0, ¥]{L \in[0, \infty]} and \mathfrakm{\mathfrak{m}} is a positive, possibly unbounded, Borel measure supported on [0, L]; we think of L as the length of the string and of \mathfrakm{\mathfrak{m}} as its mass density. To each string a differential operator acting in the space L2(\mathfrakm){L^2(\mathfrak{m})} is associated. Namely, the Kreĭn–Feller differential operator -D\mathfrakmDx{-D_{\mathfrak{m}}D_x} ; its eigenvalue equation can be written, e.g., as
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