共查询到10条相似文献,搜索用时 296 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.
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
3.
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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4.
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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5.
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.
$$
where $f(x,u)=\lambda K(x)|u|^{q-2}u+Q(x)|u|^{4}u$, $a>0,~b,~\mu\geq0$ are constants, $\alpha\in(0,3)$, $p\in[2,3),~q\in[2p,6)$ and $\varepsilon,~\lambda>0$ are parameters. Under some mild conditions on $V(x),~K(x)$ and $Q(x)$, we prove that the above system possesses a ground state solution $u_{\varepsilon}$ with exponential decay at infinity for $\lambda>0$ and $\varepsilon$ small enough. Furthermore, $u_{\varepsilon}$ concentrates around a global minimum point of $V(x)$ as $\varepsilon\rightarrow0$. The methods used here are based on minimax theorems and the concentration-compactness principle of Lions. Our results generalize and improve those in Liu and Guo (Z Angew Math Phys 66: 747-769, 2015), Zhao and Zhao (Nonlinear Anal 70: 2150-2164, 2009) and some other related literature. 相似文献
6.
关于Fujita型反应扩散方程组的Cauchy问题 总被引:5,自引:1,他引:5
本文研究Fujita型反应扩散方程组ut-Δu=α1|u|q1-1u+β1|v|p1-1v,(x∈RN,t>0),vt-Δv=α2|u|q2-1u+β2|v|p2-1v,u(x,0)=u0(x)0,v(x,0)=v0(x)0,(x∈RN)Lp解的整体存在性和有限时间Blow up问题.这里qi>1,pi>1(i=1,2),α10,α2>0,β1>0,β20,1p+∞. 相似文献
7.
The present article is concerned with the following nonlocal elliptic equation involving concave and convex terms,By means of the variational approach, we prove that the above problem admits a sequence of infinitely many solutions under suitable assumptions.
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$$\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.
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
9.
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
10.
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