共查询到20条相似文献,搜索用时 140 毫秒
1.
本文在无边界流的光滑有界区域$\Omega\subset\mathbb{R}^n~(n>2)$上研究了具有奇异灵敏度及logistic源的抛物-椭圆趋化系统$$\left\{\begin{array}{ll}u_t=\Delta u-\chi\nabla\cdot(\frac{u}{v}\nabla v)+r u-\mu u^k,&x\in\Omega,\,t>0,\\ 0=\Delta v-v+u,&x\in\Omega,\,t>0\end{array}\right.$$ 其中$\chi$, $r$, $\mu>0$, $k\geq2$. 证明了若当$r$适当大, 则当$t\rightarrow\infty$时该趋化系统全局有界解呈指数收敛于$((\frac{r}{\mu})^{\frac{1}{k-1}}, (\frac{r}{\mu})^{\frac{1}{k-1}})$. 相似文献
2.
本文首先引入满足如下条件$$-\frac{qzD_{q}f(z)}{f(z)}\prec \varphi (z)$$和$$\frac{-(1-\frac{\alpha }{q})qzD_{q}f(z)+\alpha qzD_{q}[zD_{q}f(z)]}{(1-\frac{\alpha}{q})f(z)-\alpha zD_{q}f(z)}\prec \varphi (z)~(\alpha \in\mathbb{C}\backslash (0,1],\ 0
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3.
假设 $\Omega=B_R:=\{x\in \mathbb{R}^N:|x|0$, $ N \geq 7$, $ 2^*=\frac{2N}{N-2}$, 我们得到了如下半线性问题无穷多解的存在性: $\left\{ \begin{array}{ll} -\Delta u=\frac{\mu}{|x|^2}u+|u|^{2^*-2}u+\la u, &; x\in\Omega, \\ u=0, &; x\in \partial\Omega. \end{array} \right.$ 其中$\lambda \in \mathbb{R}, \mu \in \mathbb{R}$. 这些解由不同的节点来区分. 相似文献
4.
本文主要研究如下含非线性梯度项的非强制拟线性椭圆方程\begin{equation*}\left \{\begin{array}{rl}-\text{div}(\frac{|\nabla u|^{p-2}\nabla u}{(1+|u|)^{\theta(p-1)}})+\frac{|u|^{p-2}u|\nabla u|^{p}}{(1+|u|)^{\theta p}}=\mu,~&x\in\Omega,\\ u=0,~&x\in\partial\Omega,\end{array}\right.\end{equation*} 弱解的存在性和不存在性, 其中$\Omega\subseteq\mathbb{R}^N(N\geq3)$ 是有界光滑区域, $1
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5.
6.
本文讨论下面一类分数阶微分方程多点边值问题 $$\align &D^{\alpha}_{0+}u(t) = f(t, u(t),~D^{\alpha-1}_{0+}u(t), D^{\alpha-2}_{0+}u(t), D^{\alpha-3}_{0+}u(t)),~~t\in(0,1), \\&I^{4-\alpha}_{0+}u(0) = 0, ~D^{\alpha-1}_{0+}u(0)=\displaystyle{\sum_{i=1}^{m}}\alpha_{i}D^{\alpha-1}_{0+}u(\xi_{i}),\\&D^{\alpha-2}_{0+}u(1)=\sum\limits_ {j=1}^{n}\beta_{j} D^{\alpha-2}_{0+}u(\eta_{j}),~D^{\alpha-3}_{0+}u(1)-D^{\alpha-3}_{0+}u(0)=D^{\alpha-2}_{0+}u(\frac{1}{2}),\endalign$$其中$3<\alpha \leq 4$是一个实数.通过应用Mawhin重合度理论和构建适当的算子,得到了该边值问题解的存在性结果. 相似文献
7.
该文研究了如下的奇异椭圆方程Neumann问题$\left\{\begin{array}{ll}\disp -\Delta u-\frac{\mu u}{|x|^2}=\frac{|u|^{2^{*}(s)-2}u}{|x|^s}+\lambda|u|^{q-2}u,\ \ &;x\in\Omega,\\D_\gamma{u}+\alpha(x)u=0,&;x\in\partial\Omega\backslash\{0\},\end{array}\right.$其中$\Omega $ 是 $ R^N$ 中具有 $ C^1$边界的有界区域, $ 0\in\partial\Omega$, $N\ge5$. $2^{*}(s)=\frac{2(N-s)}{N-2}$ (该文研究了如下的奇异椭圆方程Neumann问题$\left\{\begin{array}{ll}\disp -\Delta u-\frac{\mu u}{|x|^2}=\frac{|u|^{2^{*}(s)-2}u}{|x|^s}+\lambda|u|^{q-2}u,\ \ &;x\in\Omega,\\D_\gamma{u}+\alpha(x)u=0,&;x\in\partial\Omega\backslash\{0\},\end{array}\right.$其中$\Omega $ 是 $ R^N$ 中具有 $ C^1$边界的有界区域, $ 0\in\partial\Omega$, $N\ge5$. $2^{*}(s)=\frac{2(N-s)}{N-2}$ (该文研究了如下的奇异椭圆方程Neumann问题其中Ω是RN中具有C1边界的有界区域,0∈■Ω,N≥5.2*(s)=2(N-s)/N-2(0≤s≤2)是临界Sobolev-Hardy指标, 1
0.利用变分方法和对偶喷泉定理,证明了这个方程无穷多解的存在性. 相似文献
8.
该文讨论了如下具有退化粘性的非齐次双曲守恒律方程的Cauchy问题$\left\{\begin{array}{l} u_t+f(u)_x=a^2t^\alpha u_{xx}+g(u),\ \ \ x\in{\bf R},\ \ \ t>0,\\u(x,0)=u_0(x) \in L^\infty({\bf R}).\end{array}\right.\eqno{({\rm I})}$其中$f(u), g(u)$是${\bf R}$上的光滑函数, $a>0, 0<\alpha<1$均为常数.在此条件下, 作者首先给出了Cauchy问题(I)的局部解的存在性, 再利用极值原理获得了解的$L^{\infty}$估计, 从而证明了Cauchy问题(I)整体光滑解的存在性. 相似文献
9.
我们运用扰动方法证明了带有Minkowski平均算子非局部Neumann系统$$\begin{aligned}\begin{cases}\Big(r^{N-1}\frac{u''}{\sqrt{1-u''^{2}}}\Big)''=r^{N-1}f(r, u),\\\ r\in(0, 1),\ \ \ u''(0)=0,\ \ \ u''(1)=\int_{0}^{1}u''(s)dg(s)\\\end{cases}\end{aligned}$$解的存在性, 其中$k, N\geq1$是整数, $f=(f_{1},f_{2},\ldots,f_{k}):[0, 1]\times\mathbb{R}^{k}\rightarrow\mathbb{R}^{k}$连续且$g:[0, 1]\rightarrow\mathbb{R}^{k}$是有界变差函数. 相似文献
10.
应用锥压缩锥拉伸不动点定理和Leray-Schauder 抉择定理研究了一类具有P-Laplace算子的奇异离散边值问题$$\left\{\begin{array}{l}\Delta[\phi (\Delta x(i-1))]+ q_{1}(i)f_{1}(i,x(i),y(i))=0, ~~~i\in \{1,2,...,T\}\\\Delta[\phi (\Delta y(i-1))]+ q_{2}(i)f_{2}(i,x(i),y(i))=0,\\x(0)=x(T+1)=y(0)=y(T+1)=0,\end{array}\right.$$的单一和多重正解的存在性,其中$\phi(s) = |s|^{p-2}s, ~p>1$,非线性项$f_{k}(i,x,y)(k=1,2)$在$(x,y)=(0,0)$具有奇性. 相似文献
11.
Jiafa Xu Zhongli Wei Donal O Regan Donal O''Regan Yujun Cui 《Journal of Applied Analysis & Computation》2019,9(3):1165-1182
In this paper using fountain theorems we study the existence of infinitely many solutions for fractional Schr\"{o}dinger-Maxwell equations
\[\begin{cases}
(-\Delta)^\alpha u+\lambda V(x)u+\phi u=f(x,u)-\mu g(x)|u|^{q-2}u, \text{ in } \mathbb R^3,\(-\Delta)^\alpha \phi=K_\alpha u^2, \text{ in } \mathbb R^3,
\end{cases}\]
where $\lambda,\mu >0$ are two parameters, $\alpha\in (0,1]$, $K_\alpha=\frac{\pi^{-\alpha}\Gamma(\alpha)}{\pi^{-(3-2\alpha)/2}\Gamma((3-2\alpha)/2)}$ and $(-\Delta)^\alpha$ is the fractional Laplacian. Under appropriate assumptions on $f$ and $g$ we obtain an existence theorem for this system. 相似文献
12.
Existence and concentration result for Kirchhoff equations with critical exponent and Hartree nonlinearity 下载免费PDF全文
This paper is concerned with the following Kirchhoff-type equations
$$
\left\{
\begin{array}{ll}
\displaystyle
-\big(\varepsilon^{2}a+\varepsilon b\int_{\mathbb{R}^{3}}|\nabla u|^{2}\mathrm{d}x\big)\Delta u
+ V(x)u+\mu\phi |u|^{p-2}u=f(x,u), &\quad \mbox{ in }\mathbb{R}^{3},\(-\Delta)^{\frac{\alpha}{2}} \phi=\mu|u|^{p},~u>0, &\quad \mbox{ in }\mathbb{R}^{3},\\end{array}
\right.
$$
where $f(x,u)=\lambda K(x)|u|^{q-2}u+Q(x)|u|^{4}u$, $a>0,~b,~\mu\geq0$ are constants, $\alpha\in(0,3)$, $p\in[2,3),~q\in[2p,6)$ and $\varepsilon,~\lambda>0$ are parameters. Under some mild conditions on $V(x),~K(x)$ and $Q(x)$, we prove that the above system possesses a ground state solution $u_{\varepsilon}$ with exponential decay at infinity for $\lambda>0$ and $\varepsilon$ small enough. Furthermore, $u_{\varepsilon}$ concentrates around a global minimum point of $V(x)$ as $\varepsilon\rightarrow0$. The methods used here are based on minimax theorems and the concentration-compactness principle of Lions. Our results generalize and improve those in Liu and Guo (Z Angew Math Phys 66: 747-769, 2015), Zhao and Zhao (Nonlinear Anal 70: 2150-2164, 2009) and some other related literature. 相似文献
13.
Yongtao Jing & Zhaoli Liu 《数学研究》2015,48(3):290-305
Let $1
0.$ This is in sharp contrast to D'Aprile and Mugnai's non-existence results. 相似文献
14.
Uniqueness and existence of solutions for a singular system with nonlocal operator via perturbation method 下载免费PDF全文
Kamel Saoudi Mouna Kratou Eadah AlZahrani 《Journal of Applied Analysis & Computation》2020,10(4):1311-1325
In this work, we investigate the existence and the uniqueness of solutions for the nonlocal elliptic system involving a singular nonlinearity as follows:
$$
\left\{\begin{array}{ll}
(-\Delta_p)^su = a(x)|u|^{q-2}u +\frac{1-\alpha}{2-\alpha-\beta} c(x)|u|^{-\alpha}|v|^{1-\beta}, \quad
\text{in }\Omega,\ (-\Delta_p)^s v= b(x)|v|^{q-2}v +\frac{1-\beta}{2-\alpha-\beta} c(x)|u|^{1-\alpha}|v|^{-\beta}, \quad
\text{in }\Omega,\ u=v
= 0 ,\;\;\mbox{ in }\,\mathbb{R}^N\setminus\Omega,
\end{array}
\right.
$$
where $\Omega $ is a bounded domain in $\mathbb{R}^{n}$ with smooth boundary, $0<\alpha <1,$ $0<\beta <1,$ $2-\alpha -\beta
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15.
In this paper, we study the Holder regularity of weak solutions to the Dirichlet problem associated with the regional fractional Laplacian (-△)αΩ on a bounded open set Ω ■R(N ≥ 2) with C(1,1) boundary ■Ω. We prove that when f ∈ Lp(Ω), and g ∈ C(Ω), the following problem (-△)αΩu = f in Ω, u = g on ■Ω, admits a unique weak solution u ∈ W(α,2)(Ω) ∩ C(Ω),where p >N/2-2α and 1/2< α < 1. To solve this problem, we consider it into two special cases, i.e.,g ≡ 0 on ■Ω and f ≡ 0 in Ω. Finally, taking into account the preceding two cases, the general conclusion is drawn. 相似文献
16.
For ordinals α beginning a Σ1 gap in $\mathrm{L}(\mathbb {R})$, where $\Sigma _{1}^{\mathrm{J}_{\alpha }(\mathbb {R})}$ is closed under number quantification, we give an inner model‐theoretic proof that every thin $\Sigma _{1}^{\mathrm{J}_{\alpha }(\mathbb {R})}$ equivalence relation is $\Delta _{1}^{\mathrm{J}_{\alpha }(\mathbb {R})}$ in a real parameter from the (optimal) hypothesis $\mathsf {AD}^{\mathrm{J}_{\alpha }(\mathbb {R})}$. 相似文献
17.
A NECESSARY AND SUFFICIENT CONDITION OF EXISTENCE OF GLOBAL SOLUTIONS FOR SOME NONLINEAR HYPERBOLIC EQUATIONS 总被引:2,自引:0,他引:2
Zhang Quande 《数学年刊B辑(英文版)》1995,16(4):461-468
ANECESSARYANDSUFFICIENTCONDITIONOFEXISTENCEOFGLOBALSOLUTIONSFORSOMENONLINEARHYPERBOLICEQUATIONS¥ZHANGQUANDE(DepartmentofMathe... 相似文献
18.
LetΩRn be a bounded domain with a smooth boundary.We consider the longtime dynamics of a class of damped wave equations with a nonlinear memory term utt+αut-△u-∫0t 0μ(t-s)|u(s)| βu(s)ds + g(u)=f.Based on a time-uniform priori estimate method,the existence of the compact global attractor is proved for this model in the phase space H10(Ω)×L2(Ω). 相似文献
19.
刘桥 《数学年刊A辑(中文版)》2014,35(5):591-612
考虑了R~n上n(n≥2)维向列型液晶流(u,d)当初值属于Q_α~(-1)(R~n,R~n)×Q_α(R~n,S~2)(其中α∈(0,1))时Cauchy问题的适定性,这里的Q_α(R~n)最早由Essen,Janson,Peng和Xiao(见[Essen M,Janson S,Peng L,Xiao J.Q space of several real variables,Indiana Univ Math J,2000,49:575-615])引入,是指由R~n中满足的所有可测函数f全体所组成的空间.上式左端在取遍Rn中所有以l(I)为边长且边平行于坐标轴的立方体I的全体中取上确界,而Q_α~(-1)(R~n):=▽·Q_α(R~n).最后证明了解(u,d)在类C([0,T);Q_(α,T)~(-1)(R~n,R~n))∩L_(loc)~∞((0,T);L~∞(R~n,R~n))×C([0,T);Q_α,T(R~n,S~2))∩L_(loc)~∞((0,T);W~(1,∞)(R~n,S~2))(其中0T≤∞)中是唯一的. 相似文献
20.
Nitsche证明了共形双曲度量的孤立奇点要么是锥奇点,要么是尖奇点,二者必其一(Nitsche J.über die isolierten singularit?ten der L?sungen von△u=e~u [J]. Math Z, 1957, 68(3):316-324.).本文利用展开映射证明了在孤立奇点附近存在复坐标z,使得度量要么为(4α~2|z|~(2α-2))/((1-|z|~(2α))~2)|dz|~2,其中α 0,要么为|z|~(-2)(ln|z|)~(-2)|dz|~2. 相似文献