共查询到20条相似文献,搜索用时 31 毫秒
1.
Thomas Bartsch Shuangjie Peng 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,16(6):778-804
We study the radially symmetric Schr?dinger equation
$ - \varepsilon ^{2} \Delta u + V{\left( {|x|} \right)}u = W{\left( {|x|} \right)}u^{p} ,\quad u > 0,\;\;u \in H^{1} ({\mathbb{R}}^{N} ), $ - \varepsilon ^{2} \Delta u + V{\left( {|x|} \right)}u = W{\left( {|x|} \right)}u^{p} ,\quad u > 0,\;\;u \in H^{1} ({\mathbb{R}}^{N} ), 相似文献
2.
Huang Falun 《数学年刊B辑(英文版)》1989,10(3):332-340
In this paper the author proves a new fundamental lemma of Hardy-Lebesgne class
$\[{H^2}(\sigma )\]$ and by this lemma obtains some fundamental results of exponential stability of $\[{C_0}\]$-semigroup of bounded linear operators in Banach spaces. Specially, if $\[{\omega _s} = \sup \{ {\mathop{\rm Re}\nolimits} \lambda ;\lambda \in \sigma (A) < 0\} \]$ and $\[\sup \{ \left\| {{{(\lambda - A)}^{ - 1}}} \right\|;{\mathop{\rm Re}\nolimits} \lambda \ge \sigma \} < \infty \]$ , where \[\sigma \in ({\omega _s},0)\]) and A is the infinitesimal generator of a $\[{C_0}\]$-semigroup in a Banach space $X$, then $\[(a)\int_0^\infty {{e^{ - \sigma t}}\left| {f({e^{tA}}x)} \right|} dt < \infty \]$, $\[\forall f \in {X^*},x \in X\]$; (b) there exists $\[M > 0\]$ such that $\[\left\| {{e^{tA}}x} \right\| \le N{e^{\sigma t}}\left\| {Ax} \right\|\]$, $\[\forall x \in D(A)\]$; (c) there
exists a Banach space $\[\hat X \supset X\]$ such that $\[\left\| {{e^{tA}}x} \right\|\hat x \le {e^{\sigma t}}\left\| x \right\|\hat x,\forall x \in X.\]$. 相似文献
3.
Zamira Abdikalikova Ryskul Oinarov Lars-Erik Persson 《Czechoslovak Mathematical Journal》2011,61(1):7-26
We consider a new Sobolev type function space called the space with multiweighted derivatives $
W_{p,\bar \alpha }^n
$
W_{p,\bar \alpha }^n
, where $
\bar \alpha
$
\bar \alpha
= (α
0, α
1,…, α
n
), α
i
∈ ℝ, i = 0, 1,…, n, and $
\left\| f \right\|W_{p,\bar \alpha }^n = \left\| {D_{\bar \alpha }^n f} \right\|_p + \sum\limits_{i = 0}^{n - 1} {\left| {D_{\bar \alpha }^i f(1)} \right|}
$
\left\| f \right\|W_{p,\bar \alpha }^n = \left\| {D_{\bar \alpha }^n f} \right\|_p + \sum\limits_{i = 0}^{n - 1} {\left| {D_{\bar \alpha }^i f(1)} \right|}
,
|