共查询到20条相似文献,搜索用时 31 毫秒
1.
研究奇异拟线性椭圆型方程{-div(|x|~(-ap)|▽u|~(p-2)▽u) + f(x)|u|~(p-2) = g(x)\u|~(q-2)u + λh(x)|u|~(r-2),x R~N,u(x) 0,x∈ R~N,其中λ0是参数,1pN(N3),1rpgp*=0a(N—p)/p,p*=Np/{N~pd),aa+l,d=a+l-60,权函数f(x),g(x),h(x)满足一定的条件.利用山路引理和Ekeland变分原理证明了问题至少有两个非平凡的弱解. 相似文献
2.
本文研究快速扩散方程ut-Δum +| u|p =0的柯西问题 ,其中m ,p∈ ( 0 ,1) .对于 0
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3.
Existence and uniqueness of solutions of degenerate parabolic equations with variable exponents of nonlinearity 总被引:1,自引:0,他引:1
We prove the existence and uniqueness of weak solutions of the Dirichlet problem for the nonlinear degenerate parabolic equation
where a, b, c, and d are given functions of the arguments x, t, and u(x, t), and the exponents of nonlinearity γ(x, t) and σ(x, t) are known measurable and bounded functions of their arguments.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 4, pp. 3–19, 2006. 相似文献
4.
Huashui ZHAN 《数学年刊B辑(英文版)》2012,33(5):767-782
Consider the following Cauchy problem:u_t = div(|▽u ~m |~ p-2▽u~m),(x,t) ∈ST=R~N ×(0,T),u(x,0) = μ,x ∈R~N,where 1
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5.
Existence and concentration result for Kirchhoff equations with critical exponent and Hartree nonlinearity
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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.
$$
where $f(x,u)=\lambda K(x)|u|^{q-2}u+Q(x)|u|^{4}u$, $a>0,~b,~\mu\geq0$ are constants, $\alpha\in(0,3)$, $p\in[2,3),~q\in[2p,6)$ and $\varepsilon,~\lambda>0$ are parameters. Under some mild conditions on $V(x),~K(x)$ and $Q(x)$, we prove that the above system possesses a ground state solution $u_{\varepsilon}$ with exponential decay at infinity for $\lambda>0$ and $\varepsilon$ small enough. Furthermore, $u_{\varepsilon}$ concentrates around a global minimum point of $V(x)$ as $\varepsilon\rightarrow0$. The methods used here are based on minimax theorems and the concentration-compactness principle of Lions. Our results generalize and improve those in Liu and Guo (Z Angew Math Phys 66: 747-769, 2015), Zhao and Zhao (Nonlinear Anal 70: 2150-2164, 2009) and some other related literature. 相似文献
6.
关于Fujita型反应扩散方程组的Cauchy问题 总被引:5,自引:1,他引:5
本文研究Fujita型反应扩散方程组ut-Δu=α1|u|q1-1u+β1|v|p1-1v,(x∈RN,t>0),vt-Δv=α2|u|q2-1u+β2|v|p2-1v,u(x,0)=u0(x)0,v(x,0)=v0(x)0,(x∈RN)Lp解的整体存在性和有限时间Blow up问题.这里qi>1,pi>1(i=1,2),α10,α2>0,β1>0,β20,1p+∞. 相似文献
7.
The present article is concerned with the following nonlocal elliptic equation involving concave and convex terms,By means of the variational approach, we prove that the above problem admits a sequence of infinitely many solutions under suitable assumptions.
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$$\begin{array}{ll}- M \left(\int_\Omega \frac{1}{p(x)}|\nabla u|^{p(x)}{\rm d}x\right)\Big(\Delta_{p(x)}u\Big) \!&=\! \lambda \big(g(x)|u|^{q(x)-2}u\!-\!h(x)\\ &\quad |u|^{r(x)-2}u\big), \quad x\in \Omega,\\ & u = 0,\quad x\in \partial\Omega. \end{array}$$
8.
本文给出RN(N3)中有界光滑区域Ω上的拟线性椭圆型方程:-∑Ni=1xi·|Du|p-2uxi=λ|u|p-2u+a(x)|u|p-2u+f(x,u),x∈Ω(λ>0,p=Np/(N-p),2p<N)在边界条件:-|Du|p-2Dνu|Ω=ψ(x)|u|q-2u(q=(N-1)p/(N-p))下的多解性结果. 相似文献
9.
Mohamed Berbiche & Ali Hakem 《偏微分方程(英文版)》2012,25(1):1-20
We considered the Cauchy problem for the fractional wave-diffusion equation $$D^αu-Δ|u|^{m-1}u+(-Δ)^{β/2}D^γ|u|^{l-1}u=h(x,t)|u|^p+f(x,t)$$ with given initial data and where p > 1, 1 < α < 2, 0 < β < 2, 0 < γ < 1. Nonexistence results and necessary conditions for global existence are established by means of the test function method. This results extend previous works. 相似文献
10.
Ron Dror Suman Ganguli Robert S. Strichartz 《Journal of Fourier Analysis and Applications》1995,2(5):473-486
Let
be the centered maximal operator on the line. Through a numerical search procedure, we have conjectural best constants for
the weak-type 1-1 estimate (3/2) and the Lp estimate (the constant B(p,1) such that
We prove that these constants are lower bounds for the best constants and discuss the numerical evidence for the conjectures. 相似文献
11.
设0∈Ω∈RN,(N≥2)为有界光滑区域,利用山路定理,考虑如下一类含Hardy位势的拟线性椭圆型方程非平凡解的存在性:-△u-u△(|u|N,(N≥2)为有界光滑区域,利用山路定理,考虑如下一类含Hardy位势的拟线性椭圆型方程非平凡解的存在性:-△u-u△(|u|2)=μu/|x|2)=μu/|x|2+λg(x,u),x∈Ω,其中μ>0,λ>0为常数,g(x,u)为Caratheodory函数. 相似文献
12.
设n,m和r是满足r≥2,n≥0,m≥3的整数,且当r是奇数时,假设r≥m-1.称一个图为K1,m-free,如果它不包含以Kt,m为导出的子图.称一个图G为一个(r,n)-临界图,如果在删去G的任意n个点后,剩下G的子图都有一个r-因子,设G是一个Kl,m-free的(n+1)-连通图,且阶为|G|以及r(|G|≥n)是偶数,证明了:如果G的最小度至少是r+n+m-1,阶|G|≥8r5+n,并且对V(G)的任意独立点集{x1,x2}都有|NG(x1)∪NG(x2)|≥(|G|+n)/2,那么G是一个(r,n)-临界图.关于G的最小度和|NG(x1)∪NG(X2)|的下界是紧的。 相似文献
13.
14.
本文讨论了Ω上如下一类带临界增长的椭圆方程在拟超临界的Neumann边界条件下正解的存在性:-Div(| u |p-2 u) =λum up*-1,-| u |p-2 u ν=ψ(x)uq-1,x∈Ω,x∈Ω.这里Ω∈RN,(N≥3)是光滑有界区域, 1≤p < N,0< m < p-1,(N -1)pN - p= p*N-1 ≤q < p*,其中p* =NpN - p是W1,p(Ω)→Ls(Ω)的Sobolev临界指数,p*N-1 =(N -1)pN - p是W1,p(Ω)→Lt( Ω)的在(N-1)维流形上的临界指数,λ>0是一个正参数. 相似文献
15.
本文考虑了一类非局部椭圆型方程-△u+V(x)u=(1/|x|μ*Q(x)F(u)/|x|β)Q(x)f(u)|x|β,x∈Rx,其中V是正的连续位势函数,0<μ<2,0≤β<1/2,2β+μ≤2,F(s)是f(s)的原函数.假设非线性项f(s)满足Trudinger-Moser型次临界指数增长,利用变分方法证明了该方程基态解的存在性. 相似文献
16.
On ground state of fractional $p$-Kirchhoff equation involving subcritical and critical exponential growth
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In this paper, we concern the existence of nontrivial ground state solutions of
fractional $p$-Kirchhoff equation
$$\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
17.
利用非光滑临界点理论 ,本文证明了一类临界增长非线性椭圆方程-div(A(x ,u) | u|p-2 u) 1pA′u(x ,u) | u|p =g(x ,u) |u|p -2 u ,u=0 , Ω ; Ω 非平凡正解的存在性 .其中 1
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18.
J. R. Cannon 《Annali di Matematica Pura ed Applicata》1964,66(1):155-165
Summary Let u(x, t) satisfy the heat equation in 0<x<1, 0<t≤T. Let u(x, 0)=0 for 0<x<1 and let |u(0, t)|<ε, | ux(0, t) |<ε, and | u(1, t) |<M for 0≤t≤T. Then,
, where M1 and β(x) are given explicitly by simple formulas. The application of the a priori bound to obtain error estimates for a numerical
solution of the Cauchy problem for the heat equation with u(x, 0)=h(x), u(0, t)=f(t), and ux(0, t)=g(t) is discussed.
Work performed under the auspices of the U. S. Atomic Energy Commission. 相似文献
19.
含临界指数的类p-Laplacian方程无穷多解的存在性 总被引:1,自引:0,他引:1
考虑如下一类含临界指数的类p-Laplacian方程-div(a(|Du|~p)|Du|~(p-2)Du)=:-- |u|~(p~*-2)u+λf(x,u),u∈W_0~(1,p)(Ω),其中Ω∈R~N(N≥2)为有界光滑区域,a:R~+→R为连续函数.由于问题失去紧性,对Palais-Smale序列的分析需要一点技巧.本文利用Lions的集中紧原理,证明了相应泛函I_λ满足(PS)_c条件,再应用Clark临界点定理和亏格的性质,证明了方程无穷多解的存在性.进一步,得到当λ充分小时一个特殊的特征函数的存在性. 相似文献
20.
R~N上临界增长的椭圆方程无穷多解的存在性 总被引:3,自引:0,他引:3
本文证明了RN上的拟线性椭圆型方程-div(|Du|p-2Du)+|u|p-2u=λ(x)·|u|α-2u+a(x)|u|s-2u+b(x)|u|p*-2u在W1,p(RN)中无穷多解的存在性,其中N≥3,2≤p相似文献