共查询到19条相似文献,搜索用时 531 毫秒
1.
在本文中,通过运用离散的Arzel\''{a}-Ascoli引理和锥上的不动点定理,我们讨论了无限区间上二阶离散Sturm-Liouville边值问题$$\left\{\begin{array}{l}\Delta^{2}u(x-1)=f(x,u(x),\Delta u(x-1)),~~x\in\mathbb{N},\\ u(0)-a\Delta u(0)=B,~~\Delta u(\infty)=C\end{array}\right.$$ 正解的存在性,其中$\Delta u(x)=u(x+1)-u(x)$是前向差分算子,$\mathbb{N}=\{1,2,\ldots,\infty\}$且$f:\mathbb{N}\times\mathbb{R_{+}}\times\mathbb{R_{+}}\to\mathbb{R_{+}}$连续,$a>0, B, C$ 为非负实数,$\mathbb{R_{+}}=[0,+\infty)$, $\Delta u(\infty)=\lim_{x\rightarrow\infty}\Delta u(x)$. 相似文献
2.
在本文,作为著名的R\''enyi公式(其刻画了标号连通单圈图的计数显式)的自然推广,我们研究了标号匀称$(k+1)$秩$(p,~q)$超单圈的计数问题,给出了如下的计数显式:$$U_{p,~q}^{(k+1)}=\begin{cases} \frac{p!}{2[(k-1)!]^q}\cdot\sum_{t=2}^q \frac{q^{q-t-1}\cdot sgn(tk-2)}{(q-t)!}, & p=qk, \\ 0,& p\neq qk, \end{cases}$$其中$k,~p,~q$均为正整数. 相似文献
3.
本文我们考虑如下二阶奇异差分边值问题\begin{equation*}\begin{cases}-\Delta^{2} u(t-1)=\lambda g(t)f(u) ,\ t\in [1,T]_\mathbb{Z},\\u(0)=0,\\ \Delta u(T)+c(u(T+1))u(T+1)=0,\end{cases}\end{equation*}正解的存在性. 其中, $\lambda>0$, $f:(0,\infty)\rightarrow \mathbb{R}$ 是连续的,且允许在~$0$ 处奇异.通过引入一个新的全连续算子, 我们建立正解的存在性. 相似文献
4.
该文首先研究具有脉冲的线性Dirichlet边值问题
$\left\{
\begin{array}{ll}
x'(t)+a(t)x(t)=0, t\neq \tau_{k}, \ \Delta x(\tau_{k})=c_{k}x(\tau_{k}),\ \Delta x'(\tau_{k})=d_{k}x(\tau_{k}), \ x(0)=x(T)=0,
\end{array}
\right. (k=1,2\cdots,m)
$
给出该Dirichlet边值问题仅有零解的两个充分条件, 其中$a:[0,T]\rightarrow R$, $c_{k}, d_{k}, k=1,2,$ $\cdots,m$是常数, 该文首先研究具有脉冲的线性Dirichlet边值问题
$$\left\{
\begin{array}{ll}
x'(t)+a(t)x(t)=0, t\neq \tau_{k}, \ \Delta x(\tau_{k})=c_{k}x(\tau_{k}),\ \Delta x'(\tau_{k})=d_{k}x(\tau_{k}), \ x(0)=x(T)=0,
\end{array}
\right. (k=1,2\cdots,m)
$$
给出该Dirichlet边值问题仅有零解的两个充分条件, 其中$a:[0,T]\rightarrow R$, $c_{k}, d_{k}, k=1,2,$ $\cdots,m$是常数, $0<\tau_{1}<\tau_{2}\cdots<\tau_{m}<T$为脉冲时刻. 其次利用上面的线性边值问题仅有零解这个性质和Leray-Schauder度理论, 研究具有脉冲的非线性Dirichlet边值问题
$$\left\{
\begin{array}{ll}
x'(t)+f(t,x(t))=0, t\neq \tau_{k}, \ \Delta x(\tau_{k})=I_{k}(x(\tau_{k})), \ \Delta x'(\tau_{k})=M_{k}(x(\tau_{k})), \ x(0)=x(T)=0
\end{array}
\right. (k=1,2\cdots,m)
$$ 解的存在性和唯一性, 其中 $f\in C([0,T]\times
R,R)$, $I_{k},M_{k}\in C(R, R),k=1,2,\cdots,m$.
该文主要定理的一个推论将经典的Lyaponov不等式比较完美地推广到脉冲系统. 相似文献
5.
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
6.
本文研究了分数阶薛定谔-泊松系统$$\left\{\begin{array}{l}(-\Delta)^su+u+\phi u=\lambda f(u)\ \text {in} \ \mathbb {R}^3, \\ (-\Delta)^{\alpha}\phi =u^2\ \text {in} \ \mathbb {R}^3\emph{},\end{array}\right. $$ 非零解的存在性, 其中$s\in (\frac{3}{4},1), \alpha\in(0,1),\lambda$ 是正参数, $(-\Delta)^s,(-\Delta)^{\alpha}$是分数阶拉普拉斯算子. 在一定的假设条件下, 利用扰动法和Morse迭代法, 得到了系统至少一个非平凡解. 相似文献
7.
在本文中,我们研究了带有质量约束条件的基尔霍夫方程规范解的存在性问题, $$-\Big(a+b \int_{\mathbb{R}^{3}}|\nabla u|^{2} \text{d} x\Big)\Delta u=\lambda u+\mu|u|^{q-2} u+|u|^{p-2} u,~~x\in \mathbb{R}^{3},$$ 其中质量约束条件为$$S_{c}:=\Big\{u \in H^{1}(\mathbb{R}^{3}):\int_{\mathbb{R}^{3}}|u|^{2} \text{d} x=c\Big\},$$ 这里$a$, $b$, $c>0$, $\mu\in \mathbb{R}$, $2
0$, 当$(p, q)$ 属于$\mathbb{R}^{2}$中的某个域时. 我们通过使用约束最小化、集中紧性原理和Minimax方法证明了规范解的存在性.我们部分地扩展了已经被研究的结果. 相似文献
8.
9.
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, $1
相似文献
10.
给定一个赋权图$G=(V,E;w,c)$以及图$G$的一个支撑子图$G_{1}=(V,E_{1})$,这里源点集合$S=\{s_{1},s_{2},\cdots,s_{k}\}\subseteq V$,权重函数$w:E\rightarrow\mathbb{R}^{+}$,费用函数$c:E\setminus E_{1}\rightarrow\mathbb{Z}^{+}$和一个正整数$B$,本文考虑两类限制性多源点偏心距增广问题,具体叙述如下:(1)限制性多源点最小偏心距增广问题是要寻找一个边子集$E_{2}\subseteq E\setminus E_{1}$,满足约束条件$c(E_{2})$$\leq$$B$,目标是使得子图$G_{1}\cup E_{2}$上源点集$S$中顶点偏心距的最小值达到最小;(2)限制性多源点最大偏心距增广问题是要寻找一个边子集$E_{2}\subseteq E\setminus E_{1}$,满足约束条件$c(E_{2})$$\leq$$B$,目标是使得子图$G_{1}\cup E_{2}$上源点集$S$中顶点偏心距的最大值达到最小。本文设计了两个固定参数可解的常数近似算法来分别对上述两类问题进行求解。 相似文献
11.
Petru Jebelean Constantin Popa Călin Şerban 《NoDEA : Nonlinear Differential Equations and Applications》2014,21(2):289-304
We are concerned with extremal solutions for the mixed boundary value problem $$-\left(r^{N-1}\phi(u')\right)' = r^{N-1} g(r, u), \quad u'(0) = 0 = u(R),$$ where ${g : [0, R] \times \mathbb{R} \to \mathbb{R}}$ is a continuous function and ${\phi : (-\eta, \eta) \to \mathbb{R}}$ is an increasing homeomorphism with ${\phi(0) = 0.}$ We prove the existence of minimal and maximal solutions in presence of well-ordered lower and upper solutions and develop a numerical algorithm for theirs approximation. Also, we provide numerical experiments confirming the theoretical aspects. 相似文献
12.
This paper is concerned with the existence of positive solutions of the third-order boundary value problem with full nonlinearity where \(f:[0,1]\times \mathbb {R}^+\times \mathbb {R}^+\times \mathbb {R}^-\rightarrow \mathbb {R}^+\) is continuous. Under some inequality conditions on f as |(x, y, z)| small or large enough, the existence results of positive solution are obtained. These inequality conditions allow that f(t, x, y, z) may be superlinear, sublinear or asymptotically linear on x, y and z as \(|(x,y,z)|\rightarrow 0\) and \(|(x,y,z)|\rightarrow \infty \). For the superlinear case as \(|(x,y,z)|\rightarrow \infty \), a Nagumo-type growth condition is presented to restrict the growth of f on y and z. Our discussion is based on the fixed point index theory in cones.
相似文献
$$\begin{aligned} \left\{ \begin{array}{lll} u'''(t)&{}=f(t,u(t),u'(t),u''(t)),\quad t\in [0,1],\\ u(0)&{}=u'(1)=u''(1)=0, \end{array}\right. \end{aligned}$$
13.
In this paper, we study the existence of nodal solutions for the following problem:-(φ_p(x′))′= α(t)φ_p(x~+) + β(t)φ_p(x~-) + ra(t)f(x), 0 t 1,x(0) = x(1) = 0,where φ_p(s) = |s|~(p-2)s, a ∈ C([0, 1],(0, ∞)), x~+= max{x, 0}, x~-=- min{x, 0}, α(t), β(t) ∈C[0, 1]; f ∈ C(R, R), sf(s) 0 for s ≠ 0, and f_0, f_∞∈(0, ∞), where f_0 = lim_|s|→0f(s)/φ_p(s), f_∞ = lim|s|→+∞f(s)/φ_p(s).We use bifurcation techniques and the approximation of connected components to prove our main results. 相似文献
14.
In this paper, by using Krasnoselskii''s fixed-point theorem, some sufficient conditions of existence of positive solutions for the following fourth-order nonlinear Sturm-Liouville eigenvalue problem:\begin{equation*}\left\{\begin{array}{lll}
\frac{1}{p(t)}(p(t)u'')''(t)+ \lambda f(t,u)=0, t\in(0,1),
\\ u(0)=u(1)=0,
\\ \alpha u''(0)- \beta \lim_{t \rightarrow 0^{+}} p(t)u''(t)=0,
\\ \gamma u''(1)+\delta\lim_{t \rightarrow 1^{-}} p(t)u''(t)=0,
\end{array}\right.\end{equation*}
are established, where $\alpha,\beta,\gamma,\delta \geq 0,$ and $~\beta\gamma+\alpha\gamma+\alpha\delta >0$.
The function $p$ may be singular at $t=0$ or $1$, and $f$ satisfies Carath\''{e}odory condition. 相似文献
15.
Pedro M. Santos 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(3):327-353
An integral representation for the functional
is obtained. This problem is motivated by equilibria issues in micromagnetics.
相似文献
16.
In this paper, we consider the stochastic heat equation of the form $$\frac{\partial u}{\partial t}=(\Delta_\alpha+\Delta_\beta)u+\frac{\partial f}{\partial x}(t,x,u)+\frac{\partial^2W}{\partial t\partial x},$$ where $1<\beta<\alpha< 2$, $W(t,x)$ is a fractional Brownian sheet, $\Delta_\theta:=-(-\Delta)^{\theta/2}$ denotes the fractional Lapalacian operator and $f:[0,T]\times \mathbb{R}\times \mathbb{R}\rightarrow\mathbb{R}$ is a nonlinear measurable function. We introduce the existence, uniqueness and H\"older regularity of the solution. As a related question, we consider also a large deviation principle associated with the above equation with a small perturbation via an equivalence relationship between Laplace principle and large deviation principle. 相似文献
17.
Multiple solutions for a nonhomogeneous Schrodinger-Poisson system with concave and convex nonlinearities
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In this paper, we consider the following nonhomogeneous Schrodinger-Poisson equation
$$
\left\{
- \Delta u +V(x)u+\phi(x)u =-k(x)|u|^{q-2}u+h(x)|u|^{p-2}u+g(x), &x\in \mathbb{R}^3,\\ \Delta \phi =u^2, \quad \lim_{|x|\rightarrow +\infty}\phi(x)=0, & x\in \mathbb{R}^3,
\right.
$$
where $1
相似文献
18.
In this paper,the authors obtain the existence of one-signed periodic solutions of the first-order functional difference equation ?u(n) = a(n)u(n)-λb(n)f(u(n-τ(n))),n ∈ Z by using global bifurcation techniques,where a,b:Z → [0,∞) are T-periodic functions with ∑T n=1 a(n) 0,∑T n=1 b(n) 0;τ:Z → Z is T-periodic function,λ 0 is a parameter;f ∈ C(R,R) and there exist two constants s_2 0 s_1 such that f(s_2) = f(0) = f(s_1) = 0,f(s) 0 for s ∈(0,s_1) ∪(s_1,∞),and f(s) 0 for s ∈(-∞,s_2) ∪(s_2,0). 相似文献
19.
On ground state of fractional $p$-Kirchhoff equation involving subcritical and critical exponential growth
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In this paper, we concern the existence of nontrivial ground state solutions of
fractional $p$-Kirchhoff equation
$$\left\{\begin{array}{ll}
m\left(\|u\|^p\right) [(-\Delta)_p^su+V(x)|u|^{p-2}u]
=f(x,u) \quad\text{in}\, \mathbb{R}^N, \vspace{0.2
cm}\\ \|u\|=\left(\int_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy +\int_{\mathbb{R}^N}V(x)|u|^pdx\right)^{\frac{1}{p}},
\end{array}\right.$$
where $m:[0,+\infty)\rightarrow [0,+\infty)$ is a continuous function, $(-\Delta)_p^s$ is the fractional $p$-Laplacian operator with $0相似文献