共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper we discuss the global behaviour of some connected sets of solutions of a broad class of second order quasilinear elliptic equations
for where is a real parameter and the function u is required to satisfy the condition
The basic tool is the degree for proper Fredholm maps of index zero in the form due to Fitzpatrick, Pejsachowicz and Rabier.
To use this degree the problem must be expressed in the form where J is an interval, X and Y are Banach spaces and F is a map which is Fredholm and proper on closed bounded subsets. We use the usual spaces and . Then the main difficulty involves finding general conditions on and b which ensure the properness of F. Our approach to this is based on some recent work where, under the assumption that and b are asymptotically periodic in x as $\left| x\right| \rightarrow\infty$, we have obtained simple conditions which are necessary and sufficient for to be Fredholm and proper on closed bounded subsets of X. In particular, the nonexistence of nonzero solutions in X of the asymptotic problem plays a crucial role in this issue. Our results establish the bifurcation of global branches of
solutions for the general problem. Various special cases are also discussed. Even for semilinear equations of the form
our results cover situations outside the scope of other methods in the literature.
Received March 30, 1999; in final form January 17, 2000 / Published online February 5, 2001 相似文献
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Hengwu Zheng 《Semigroup Forum》2011,83(3):457-467
As a generalization of Preston’s kernel normal systems, P\mathcal{P}-kernel normal systems for P\mathcal{P}-inversive semigroups are introduced, and strongly regular P\mathcal{P}-congruences on P\mathcal{P}-inversive semigroups in terms of their P\mathcal{P}-kernel normal systems are characterized. These results generalize the corresponding results for P\mathcal{P}-regular semigroups and P\mathcal{P}-inversive semigroups. 相似文献
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Paul Larson 《Archive for Mathematical Logic》2000,39(7):541-568
Given a stationary subset T of , let be the set of ordinals in the interval which are necessarily in the image of T by any embedding derived from the nonstationary ideal. We consider the question of the size of , givenT, and use Martin's Maximum and to give some answers.
Received: 23 November 1998 相似文献
6.
We construct a global solution with $\mathcal {C}^{k}$‐estimates for the $\bar{\partial }$‐equation on q‐convex intersections. 相似文献
7.
William R. Brian 《Mathematical Logic Quarterly》2013,59(3):167-176
This paper describes a new and user‐friendly method for constructing models of non‐well‐founded set theory. Given a sufficiently well‐behaved system θ of non‐well‐founded set‐theoretic equations, we describe how to construct a model Mθ for $\mathsf {ZFC}^-$ in which θ has a non‐degenerate solution. We shall prove that this Mθ is the smallest model for $\mathsf {ZFC}^-$ which contains $\mathbf {V}$ and has a non‐degenerate solution of θ. 相似文献
8.
A New Proof of Diophantine Equation $\Bigg( \begin{matrix} n \\ 2 \end{matrix} \Bigg) = \Bigg( \begin{matrix} m \\ 4 \end{matrix} \Bigg)$ 下载免费PDF全文
Huilin Zhu 《数学研究通讯:英文版》2009,25(3):282-288
By using algebraic number theory and $p$-adic analysis method, we give a new and simple proof of Diophantine equation $\Bigg( \begin{matrix} n \\ 2 \end{matrix} \Bigg) =\Bigg( \begin{matrix} m \\ 4 \end{matrix} \Bigg)$. 相似文献
9.
对自正交模类$\mathcal{W}$,引入了强$\mathcal{W}$-Gorenstein复形的概念.给出了强$\mathcal{W}$-Gorenstein复形的刻画,并将其应用到强Gorenstein内射复形. 相似文献
10.
David Burguet 《Inventiones Mathematicae》2011,186(1):191-236
We prove that C2\mathcal{C}^{2} surface diffeomorphisms have symbolic extensions, i.e. topological extensions which are subshifts over a finite alphabet.
Following the strategy of Downarowicz and Maass (Invent. Math. 176:617–636, 2009) we bound the local entropy of ergodic measures in terms of Lyapunov exponents. This is done by reparametrizing Bowen balls
by contracting maps in a approach combining hyperbolic theory and Yomdin’s theory. 相似文献
11.
In this paper, the irreducible p, q‐representations of the Lie algebras $\mathcal {G}(0,1)$ and $\mathcal {G}(0,0)$ are discussed. We prove two theorems that classify certain irreducible p, q‐representations of these Lie algebras and construct their one variable models in terms of p, q‐derivative and dilation operators. As an application, we derive a p, q‐special function identity based on one such model. 相似文献
12.
Multiple sign-changing solutions for a class of semilinear elliptic equations in $\mathbb{R}^{N}$ 下载免费PDF全文
In this paper, we study the following semilinear elliptic equations $$-\triangle u+V(x)u=f(x,u), \ \ x\in \mathbb{R}^{N},$$ where $V\in C(\mathbb{R}^{N}, \mathbb{R})$ and $f\in C(\mathbb{R}^{N}\times\mathbb{R}, \mathbb{R})$. Under some suitable conditions, we prove that the equation has three solutions of mountain pass type: one positive, one negative, and sign-changing. Furthermore, if $f$ is odd with respect to its second variable, this problem has infinitely many sign-changing solutions. 相似文献
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设$\mathcal{F}$是一个群类. 群$G$的子群$H$称为在$G$中$\mathcal{F}$-S-可补的,如果存在$G$的一个子群$K$,使得$G=HK$且$K/K\cap{H_G}\in\mathcal{F}$, 其中$H_G=\bigcap_{g\in G}H^g$是包含在$H$中的$G$的最大正规子群.本文利用子群的$\mathcal{F}$-S-可补性, 给出了有限群的可解性, 超可解性和幂零性的一些新的刻画. 应用这些结果, 我们可以得到一系列推论, 其中包括有关已知的著名结果. 相似文献
15.
Qingyan WU 《数学年刊B辑(英文版)》2010,31(2):201-210
The author determines the real-analytic infinitesimal CR automorphisms of a class of non-homogeneous rigid hypersurfaces in C^N+1 near the origin, and the connected component containing the identity transformation of all locally holomorphic automorphisms of these hypersurfaces near the origin. 相似文献
16.
In this paper, the sharp estimates of all homogeneous expansions for f are established, where f(z) = (f
1(z), f
2(z), …, f
n
(z))′ is a k-fold symmetric quasi-convex mapping defined on the unit polydisk in ℂ
n
and
$
\begin{gathered}
\frac{{D^{tk + 1} + f_p \left( 0 \right)\left( {z^{tk + 1} } \right)}}
{{\left( {tk + 1} \right)!}} = \sum\limits_{l_1 ,l_2 ,...,l_{tk + 1} = 1}^n {\left| {apl_1 l_2 ...l_{tk + 1} } \right|e^{i\tfrac{{\theta pl_1 + \theta pl_2 + ... + \theta pl_{tk + 1} }}
{{tk + 1}}} zl_1 zl_2 ...zl_{tk + 1} ,} \hfill \\
p = 1,2,...,n. \hfill \\
\end{gathered}
$
\begin{gathered}
\frac{{D^{tk + 1} + f_p \left( 0 \right)\left( {z^{tk + 1} } \right)}}
{{\left( {tk + 1} \right)!}} = \sum\limits_{l_1 ,l_2 ,...,l_{tk + 1} = 1}^n {\left| {apl_1 l_2 ...l_{tk + 1} } \right|e^{i\tfrac{{\theta pl_1 + \theta pl_2 + ... + \theta pl_{tk + 1} }}
{{tk + 1}}} zl_1 zl_2 ...zl_{tk + 1} ,} \hfill \\
p = 1,2,...,n. \hfill \\
\end{gathered}
相似文献
17.
We provide a sufficient condition for a measure on the real line to satisfy a modified logarithmic Sobolev inequality, thus extending the criterion of Bobkov and Götze. Under mild assumptions the condition is also necessary. Concentration inequalities are derived. This completes the picture given in recent contributions by Gentil, Guillin and Miclo. 相似文献
18.
In this note, we study symmetry of solutions of the elliptic equation\begin{equation*} -\Delta _{\mathbb{S}^{2}}u+3=e^{2u}\ \ \hbox{on}\ \ \mathbb{S}^{2},\end{equation*} that arises in the consideration of rigidity problem of Hawking mass in general relativity. We provide various conditions under which this equation has only constant solutions, and consequently imply the rigidity of Hawking mass for stable constant mean curvature (CMC) sphere. 相似文献
20.
Emmanuel Giner 《Set-Valued and Variational Analysis》2007,15(2):125-138
We give complete characterizations of integral functionals which are Lipschitzian on a Lebesgue space L p with p ≠ ∞. When the measure is atomless, we characterize the integral functionals which are locally Lipschitzian on such Lebesgue spaces. In every cases, the Lipchitzian properties of the integral functional can be described by growth conditions on the subdifferentials of the integrand which are equivalent to Lipschitzian properties of the integrand. 相似文献
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