共查询到20条相似文献,搜索用时 46 毫秒
1.
关于Diophantine方程x3+1=py2 总被引:1,自引:0,他引:1
在素数p=3(8t+4)(8t+5)+1和p=3(8t+3)(8t+4)+1的情形下,运用初等数论的方法给出了丢番图方程x3+1=py2无正整数解的充分条件,并得到无数个6k+1型的素数p使得方程x3+1=py2无正整数解. 相似文献
2.
利用锥上的不动点定理证明了二阶Nuemann特征值问题-u″+Mu=λa(t)f(u(t))m0≤t≤1 u′(0)=u′(1)=0是的正解存在性结果. 相似文献
3.
对二阶常系数非齐次线性微分方程(其中p,q,λ,ω是实数,ω≠0;Pl(x),Pn(x)分别是l,n次实多项式),求通解的关键在于找到它的一个持解,一般高等数学教材都利用欧拉公式把恒等变形为然后根据y″+py′+qy=e~(λx)Pm(x)型方程的特解推得方程()的待解形式为这种变未知为已知间接求解的方法思路清晰,推导简便,但它涉及面较广,中;司转换较多,最终求特解时运算复杂。为了从另一方面启发思维,同时避开这些难点,下面介绍直接推导方程(1)的待解形式的方法,它直观明了,易于接受,又大大简化了求持解的运算。观察方程… 相似文献
4.
B. FISHER K. TAS 《数学学报(英文版)》2006,22(6):1639-1644
Let f and g be distributions and let gn = (g * δn)(x), where δn (x) is a certain converging to the Dirac delta function. The non-commutative neutrix product fog of f and g to be the limit of the sequence {fgn }, provided its limit h exists in the sense that sequence is defined N-lim n-∞(f(x)g,, (x), φ(x)〉 = (h(x), φ(x)},for all functions p in 2. It is proved that (x^λ+1n^px+)0(x^μ+1n^qx+)=x+^λμ1n^p+qx+,(x^λ-1n^qx-)=x-^λ+μ1n^p+qx-,for λ+μ〈-1; λ,μ, λ+μ≠-1,-2…and p,q=0,1,2…… 相似文献
5.
曹璎珞 《应用数学与计算数学学报》1990,4(1):45-52,12
本文首先给出ρ(χ)为分段线性函数时,以方程y″ λρ(x)y=0 的特征值为零点的函数ω(λ),从而给出基于分段线性逼近的中介算子法,以求方程(p(x)y′)′ λq(x)y=0之最小特征值的上、下估计值。 相似文献
6.
已知圆O:x^2+y^2=r^2,点P(x0,y0).
1.当点P在圆t时,我们知道x0x+y0y=r^2。为过点P(x0,y0)的圆O的切线方程. 相似文献
7.
Joseph A. Iaia 《偏微分方程(英文版)》2010,(1):33-67
We study capillary spreadings of thin films of liquids of power-law rheology. These satisfy ut+(u^λ+2|uxxx|^λ-1uxxx)x=0,where u (x, t) represents the thickness of the one-dimensional liquid and λ 〉 1. We look for traveling wave solutions so that u(x,t) =g(x+ct) and thus g satisfies g'''=|g-ε|^1/λ/g^1+2/λ sgn(g-ε) We show that for each ε 〉 0 there is an infinitely oscillating solution, gε, such that limt→∞ gε=ε and that gε→ g0 as ε → O, where g0≡ 0 for t ≥ 0 and g0=cλ|t|3λ/2λ+1 for t〈0 for some constant cλ. 相似文献
8.
In this paper, we prove that the second order differential equation d^2x/dt^2+x^2n_1f(x)+p(t)=0with p(t + 1) = p(t), f(x + T) = f(x) smooth and f(x) 〉 0, possesses Lagrangian stability despite of the fact that the monotone twist condition is violated. 相似文献
9.
We study the following Schrodinger-Poisson system where (Pλ){-△u+ V(x)u+λФ(x)u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф(x) =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈 +∞, V(x) and Q(x)=1 ,D.Ruiz[19] proved that(Pλ)with p∈ (2, 5) has always a positive radial solution, but (Pλ) with p E (1, 2] has solution only if λ 〉 0 small enough and no any nontrivial solution if λ≥1/4.By using sub-supersolution method,we prove that there exists λ0〉0 such that(Pλ)with p ∈(1+∞)has alaways a bound state(H^1(R^3)solution for λ∈[0,λ0)and certain functions V(x)and Q(x)in L^∞(R^3).Moreover,for every λ∈[0,λ0),the solutions uλ of (Pλ)converges,along a subsequence,to a solution of (P0)in H^1 as λ→0 相似文献
10.
Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations {[φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 are established,where [φ(x)] =(|x |p-2x) with p 1.Our result is new even when [φ(x)] = x in above problem,i.e.p = 2.Examples are presented to illustrate the effciency of the theorem in this paper. 相似文献
11.
研究一类高阶混合中立型微分方程:x(t)+ax(t-γ)-bx(t+σ)]~((m))+δ(q(t)x(t-g)+p(t)x(t+h))=0,其中a,b,γ,σ,g,h是正常数,P,q∈C(R~+,R~+),δ=士1,m≥1是整数.得到了方程振动的判据. 相似文献
12.
考虑非线性脉冲微分方程{x'(t)=x(t)[a(t)-b(t)x^p(t)],t≠tk, △x|t=tk=ckx(tk),k∈N.得到了该方程存在正周期解的充要条件为m∏k=1(1+ck)^pexp(p∫^w 0)a(σ)dσ)>1. 相似文献
13.
Multiple positive solutions for superlinear second order singular boundary value problems with derivative dependence 总被引:1,自引:1,他引:0
闫宝强 《数学物理学报(B辑英文版)》2008,28(4):851-864
The existence of at least two positive solutions is presented for the singular second-order boundary value problem
{1/p(t)( p(t)x′(t))′+Φ(t)f(t,x(t),p(t)x′(t))=0,0〈t〈1,
limt→0 p(t)x′(t)=0,x(1)=0
by using the fixed point index, where f may be singular at x = 0 and px ′= 0. 相似文献
{1/p(t)( p(t)x′(t))′+Φ(t)f(t,x(t),p(t)x′(t))=0,0〈t〈1,
limt→0 p(t)x′(t)=0,x(1)=0
by using the fixed point index, where f may be singular at x = 0 and px ′= 0. 相似文献
14.
MOUSSAOUI Abdelkrim KHODJA Brahim 《偏微分方程(英文版)》2009,22(2):111-126
In this paper, we study the existence of nontrivial solutions for the problem
{-△u=f(x,u,v)+h1(x)in Ω
-△v=g(x,u,v)+h2(x)inΩ
u=v=0 onδΩ
where Ω is bounded domain in R^N and h1,h2 ∈ L^2 (Ω). The existence result is obtained by using the Leray-Schauder degree under the following condition on the nonlinearities f and g:
{lim s,|t|→+∞f(x,s,t)/s=lim |s|,t→+∞g(x,s,t)/t=λ+1 uniformly on Ω,
lim -s,|t|→+∞f(x,s,t)/s=lim |s|,-t→+∞g(x,s,t)/t=λ-,uniformly on Ω,
where λ+,λ-∈(0)∪σ(-△),σ(-△)denote the spectrum of -△. The cases (i) where λ+ = λ_ and (ii) where λ+≠λ_ such that the closed interval with endpoints λ+,λ_ contains at most one simple eigenvatue of -△ are considered. 相似文献
{-△u=f(x,u,v)+h1(x)in Ω
-△v=g(x,u,v)+h2(x)inΩ
u=v=0 onδΩ
where Ω is bounded domain in R^N and h1,h2 ∈ L^2 (Ω). The existence result is obtained by using the Leray-Schauder degree under the following condition on the nonlinearities f and g:
{lim s,|t|→+∞f(x,s,t)/s=lim |s|,t→+∞g(x,s,t)/t=λ+1 uniformly on Ω,
lim -s,|t|→+∞f(x,s,t)/s=lim |s|,-t→+∞g(x,s,t)/t=λ-,uniformly on Ω,
where λ+,λ-∈(0)∪σ(-△),σ(-△)denote the spectrum of -△. The cases (i) where λ+ = λ_ and (ii) where λ+≠λ_ such that the closed interval with endpoints λ+,λ_ contains at most one simple eigenvatue of -△ are considered. 相似文献
15.
If the second order problem u(t) + Bu(t) + Au(t) = f(t), u(0) =u(0) = 0 has L^p-maximal regularity, 1 〈 p 〈 ∞, the analyticity of the corresponding propagator of the sine type is shown by obtaining the estimates of ‖λ(λ^2 + λB + A)^-1‖ and ‖B(λ^2 + λB + A)^-1‖ for λ∈ C with Reλ 〉 ω, where the constant ω≥ 0. 相似文献
16.
利用拓扑度理论和上下解方法讨论了一类三阶微分方程组{x′′′(t)+f1(t,y(t),x′(t),x″(t))=0,0≤t≤1,y′′′(t)+f2(t,x(t),y′(t),y″(t))=0,0≤t≤1在适当的条件下解的存在性. 相似文献
17.
本文指出文[1]中的一个失误,给出了一类半线性方程周期边值问题a(t)x″+b(t)x′+g(t,x)=e(t),x(0)-x(2π)=x′(0)-xv(2π)=0一个新的等价方程组,应用整体反函数定理得到文[1]的所有结论. 相似文献
18.
1引言考虑如下标准特征值问题:A(p)x(p)=λ(p)x(p),其中p=(p1,pN)T∈RN,A(p)=(a)(ij)(p))∈Rn×n是在p*∈RN的某邻域内解析的矩阵值函数,λ(p),x(p)为系统的特征值和特征向量.特征值关于设计参数的偏导数与特征向量关于设计参数的偏导数在模型修正[2],结构优化[16],故障诊断[8]等领域中具有重要应用.近几十年来,国内外学者在特征对导数 相似文献
19.
Let Ω IR^N, (N ≥ 2) be a bounded smooth domain, p is Holder continuous on Ω^-,
1 〈 p^- := inf pΩ(x) ≤ p+ = supp(x) Ω〈∞,
and f:Ω^-× IR be a C^1 function with f(x,s) ≥ 0, V (x,s) ∈Ω × R^+ and sup ∈Ωf(x,s) ≤ C(1+s)^q(x), Vs∈IR^+,Vx∈Ω for some 0〈q(x) ∈C(Ω^-) satisfying 1 〈p(x) 〈q(x) ≤p^* (x) -1, Vx ∈Ω ^- and 1 〈 p^- ≤ p^+ ≤ q- ≤ q+. As usual, p* (x) = Np(x)/N-p(x) if p(x) 〈 N and p^* (x) = ∞- if p(x) if p(x) 〉 N. Consider the functional I: W0^1,p(x) (Ω) →IR defined as
I(u) def= ∫Ω1/p(x)|△|^p(x)dx-∫ΩF(x,u^+)dx,Vu∈W0^1,p(x)(Ω),
where F (x, u) = ∫0^s f (x,s) ds. Theorem 1.1 proves that if u0 ∈ C^1 (Ω^-) is a local minimum of I in the C1 (Ω^-) ∩C0 (Ω^-)) topology, then it is also a local minimum in W0^1,p(x) (Ω)) topology. This result is useful for proving multiple solutions to the associated Euler-lagrange equation (P) defined below. 相似文献
1 〈 p^- := inf pΩ(x) ≤ p+ = supp(x) Ω〈∞,
and f:Ω^-× IR be a C^1 function with f(x,s) ≥ 0, V (x,s) ∈Ω × R^+ and sup ∈Ωf(x,s) ≤ C(1+s)^q(x), Vs∈IR^+,Vx∈Ω for some 0〈q(x) ∈C(Ω^-) satisfying 1 〈p(x) 〈q(x) ≤p^* (x) -1, Vx ∈Ω ^- and 1 〈 p^- ≤ p^+ ≤ q- ≤ q+. As usual, p* (x) = Np(x)/N-p(x) if p(x) 〈 N and p^* (x) = ∞- if p(x) if p(x) 〉 N. Consider the functional I: W0^1,p(x) (Ω) →IR defined as
I(u) def= ∫Ω1/p(x)|△|^p(x)dx-∫ΩF(x,u^+)dx,Vu∈W0^1,p(x)(Ω),
where F (x, u) = ∫0^s f (x,s) ds. Theorem 1.1 proves that if u0 ∈ C^1 (Ω^-) is a local minimum of I in the C1 (Ω^-) ∩C0 (Ω^-)) topology, then it is also a local minimum in W0^1,p(x) (Ω)) topology. This result is useful for proving multiple solutions to the associated Euler-lagrange equation (P) defined below. 相似文献
20.
黄丽容 《应用泛函分析学报》2009,11(4):330-333
运用集中紧性和Nehari约束方法,证明了对任意L〉0和c〉0,修正的Benjamin方程
ηt+(f(η))x+LHηxx+ηxxx=0,x,t/∈R
有一个孤立波η(x,t)=u(x-ct). 相似文献