共查询到20条相似文献,搜索用时 46 毫秒
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本文研究退化椭圆型方程-Δxu-(α+1)2|x|~(2α)Δyu=|u|~(p-1)u,(x,y)∈Rm×Rk和方程-Δxu-(α+1)2|x|~(2α)Δyu=|u|~(p-1)u,(x,y)∈Π的Liouville型定理,其中-Δx-(α+1)2|x|~(2α)Δy是Grushin算子,Π={(x,y)∈Rm×Rk:x10}或{(x,y)∈Rm×Rk:y10}.本文将证明,当1p(Q+2)/(Q-2)时,上述方程Morse指数有限的有界解只有零解,其中Q=m+(α+1)k为齐次空间的维数,因此,本文将Laplace方程的结果推广到含Grushin算子的方程. 相似文献
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吴炯圻 《数学物理学报(A辑)》2003,23(5):627-640
该文主要研究形如Δ((Δ\+nu)\+\{p-1*\}) = f(|x|, u, |u|)u\+\{-β\},\ x∈R\+2的奇异非线性多调和方程在R\+2上的正整体解,此处p>1,β≥0是常数,n是自然数,f: [AKR-]\-+×R\-+×[AKR-]\-+→R\-+是 一个连续函数,ξ\+\{α*\}:=|ξ|\+\{α-1\}ξ,ξ∈R,α>0 . 证明了这种解 u必无界且其渐进阶(当n→∞时u作为无穷大量的阶)不低于|x|\+\{2n\}log|x| ,给 出了该方程具有无穷多个其渐进阶刚好为 |x|\+\{2n\}log|x| 的正整体解的充分与充分必要条件. 这些结论可以推广到更一般的方程中去.
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This paper studies the following semilinear SchrSdinger problem -Δu v(x)u=λu-g(x)|u|^p-1u,x∈R^N It is proven that there exists a bifurcation branch of solutions for the above problem, when g(x) can possibly vanish except for a bounded domain Ω∈R^N. 相似文献
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本文用变分法和集中紧性原理获得了一类具奇异势的拟线性椭圆方程-Δ_pu=μ(|μ|~(P~*(s)-2)u)/(|x|~s) λf(x,u),u∈H_0~(1,p)(Ω)的无穷多解. 相似文献
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${\mbox{\boldmath $R$}}^N$上奇异非线性多调和方程的正整体解 总被引:7,自引:2,他引:5
本文研究形如△((△nu)(p-1) )=f(|x|,u,|(?)u|)u-β,x∈RN的奇异非线性多调和方程在RN上的正整体解,此处P>1,β≥0是常数,n是自然数,f:R × R ×R →R 是一个连续函数, ξδ*:=sign(ξ)·|ξ|δ,,ξ∈R,δ>0,给出了该类方程具有无穷多个其渐进阶刚好为|x|2n的正整体解的充分条件与必要条件.这些结论可以推广到更一般的方程. 相似文献
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该文考虑-Δu =g(x) |u|q- 2 u λ|u|p- 2 u f(x) ,x∈Ω,u| Ω =0 ,g,f∈ L∞ (Ω ) ,1
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本文研究形如△((△nu)(p-1)*)=f(|x|,u,| u|)u-β,x∈RN的奇异非线性多调和方程在RN上的正整体解,此处p>1,β≥0是常数,n是自然数,f:R+×R+×R+→R+是一个连续函数,ξδ*:=sign(ξ)·|ξ|δ,ξ∈R,δ>0,给出了该类方程具有无穷多个其渐进阶刚好为|x|2n的正整体解的充分条件与必要条件.这些结论可以推广到更一般的方程. 相似文献
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刘晓春 《数学物理学报(A辑)》2000,20(4)
讨论非线性 Schrodinger方程-Δu q(x) u =λu Q(x) |u|p- 1u x∈ RN的解的存在性 .其中 q(x) ,Q(x)满足周期性条件 ,而且 Q(x)变号 ,λ∈R落在 - Δ q的谱隙中 ,1
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We obtain new gauge-invariant forms of two-dimensional integrable systems of nonlinear equations: the Sawada-Kotera and Kaup-Kuperschmidt
system, the generalized system of dispersive long waves, and the Nizhnik-Veselov-Novikov system. We show how these forms imply
both new and well-known twodimensional integrable nonlinear equations: the Sawada-Kotera equation, Kaup-Kuperschmidt equation,
dispersive long-wave system, Nizhnik-Veselov-Novikov equation, and modified Nizhnik-Veselov-Novikov equation. We consider
Miura-type transformations between nonlinear equations in different gauges.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 160, No. 1, pp. 35–48, July, 2009. 相似文献
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Martina Chirilus-Bruckner Wolf-Patrick Düll Guido Schneider 《Journal of Mathematical Analysis and Applications》2014
Bethuel et al. and and Chiron and Rousset [3] gave very nice proofs of the fact that slow modulations in time and space of periodic wave trains of the NLS equation can approximately be described via solutions of the KdV equation associated with the wave train. Here we give a much shorter proof of a slightly weaker result avoiding the very detailed and fine analysis of , and . Our error estimates are based on a suitable choice of polar coordinates, a Cauchy–Kowalevskaya-like method, and energy estimates. 相似文献
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Young Whan Lee Byung Mun Choi 《Journal of Mathematical Analysis and Applications》2004,299(2):305-313
We obtain the super stability of Cauchy's gamma-beta functional equation
B(x,y)f(x+y)=f(x)f(y), 相似文献
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We obtain exact solutions U(x, y, z, t) of the three-dimensional sine-Gordon equation in a form that Lamb previously proposed
for integrating the two-dimensional sine-Gordon equation. The three-dimensional solutions depend on arbitrary functions F(α)
and ϕ(α,β), whose arguments are some functions α(x, y, z, t) and β(x, y, z, t). The ansatzes must satisfy certain equations. These
are an algebraic system of equations in the case of one ansatz. In the case of two ansatzes, the system of algebraic equations
is supplemented by first-order ordinary differential equations. The resulting solutions U(x, y, z, t) have an important property,
namely, the superposition principle holds for the function tan(U/4). The suggested approach can be used to solve the generalized sine-Gordon equation, which, in contrast to the classical equation,
additionally involves first-order partial derivatives with respect to the variables x, y, z, and t, and also to integrate
the sinh-Gordon equation. This approach admits a natural generalization to the case of integration of the abovementioned types
of equations in a space with any number of dimensions.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 370–377, March, 2009. 相似文献
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Alvaro H. Salas 《Applied mathematics and computation》2010,216(1):18-3836
In this paper we give exact solutions for a forced Burgers equation. We make use of the generalized Cole-Hopf transformation and the traveling wave method. 相似文献
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Discretisation of the integral equations of acoustic scattering yields a system of linear equations with full coefficient matrices. In recent years a number of fast algorithms for the solution of this system have been proposed. In this paper we present a complete analysis for a fast multipole method for the Helmholtz equation. A one-level diagonal form of the multipole method is applied to a hypersingular integral equation arising from 2d scattering theory. The error of the approximation is analysed and the results used to establish the complexity of the method. 相似文献
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We search for traveling-wave solutions of the class of PDEswhere Ap(Q),Br(Q),Cs(Q),Du(Q) and F(Q) are polynomials of Q. The basis of the investigation is a modification of the method of simplest equation. The equations of Bernoulli, Riccati and the extended tanh-function equation are used as simplest equations. The obtained general results are illustrated by obtaining exact solutions of versions of the generalized Kuramoto-Sivashinsky equation, reaction-diffusion equation with density-dependent diffusion, and the reaction-telegraph equation. 相似文献