共查询到20条相似文献,搜索用时 78 毫秒
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研究次椭圆p-Laplace方程(P>1)解的边界性质,通过建立Heisenberg群上带有区域内点到边界Carnot-Carath閛dory距离函数的Hardy型不等式,给出了有界域上次椭圆p-Laplace方程以及带非平凡位势的次椭圆p-Laplace方程的解在边界附近的若干估计. 相似文献
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关于次线性椭圆方程正解的对称性 总被引:1,自引:0,他引:1
梅海涛 《高校应用数学学报(A辑)》1999,14(2):155-160
本文利用次线性项在零点附近的凹性和可积发表和移动平面法给出一类次线性椭圆方程正解的对称性。 相似文献
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张立群 《数学物理学报(A辑)》1991,11(2):130-142
本文讨论方程正解的唯一性 作者证明了若f(u)=-u+u~p,则存在ε~*>0,使当1
0,使当|ε|<ε~*时,方程(Ⅰ)的正解是唯一的。 相似文献
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考虑半线性椭圆方程组■(1)其中A>0,Ω是有界光滑区域.f,g是定义在R_+~2:=[0,∞)×[0,∞)上的实值函数讨论在满足什么条件下此半线性椭圆方程组存在唯一的正解. 相似文献
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研究一类奇异椭圆方程问题。利用变分方法和锥理论中的混合单调方法,证明了奇异方程正解的存在性。 相似文献
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证明了一类半线性椭圆方程正解满足等周不等式,并得到了此解的最佳上界估计. 相似文献
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Zhaoyang Yin 《Monatshefte für Mathematik》2004,141(4):337-344
We prove under quite general assumptions the existence of a bounded positive solution to the semilinear Schrödinger equation in a two-dimensional exterior domain. 相似文献
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We prove the refined ABP maximum principle, comparison principle, and related existence and uniqueness theorem for the positive solutions of the Dirichlet problems of second order fully nonlinear elliptic equations on arbitrary bounded domains. 相似文献
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Alan V. Lair 《Applicable analysis》2013,92(5):431-437
We show that the equation Δu = p(x)f(u) has a positive solution on R N , N ≥ 3, satisfying <artwork name="GAPA31011ei1"> <artwork name="GAPA31011ei2"> if and only if <artwork name="GAPA31011ei3"> when ψ(r) = min{p(x): |x| = r}. The nondecreasing continuous function f satisfies f(0) = 0, f (s) > 0 for s > 0, and sup s ≥ 1 f(s)/s<∞, and the nonnegative continuous function p is required to be asymptotically radial. This extends previous results which required the function p to be constant or radial. 相似文献
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Several existence theorems on multiple positive radial solutions of the elliptic boundary value problem in an exterior domain
are obtained by using the fixed point index theory. Our conclusions are essential improvements of the results in [7], [10]
and [13]. 相似文献
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Existence and Stability Results for Renormalized Solutions to Noncoercive Nonlinear Elliptic Equations with Measure Data 总被引:1,自引:0,他引:1
In this paper we prove the existence of a renormalized solution to a class of nonlinear elliptic problems whose prototype is
where is a bounded open subset of , , is the so-called Laplace operator, , is a Radon measure with bounded variation on , , , and belong to the Lorentz spaces , and , respectively. In particular we prove the existence result under the assumption that , is small enough and , with . We also prove a stability result for renormalized solutions to a class of noncoercive equations whose prototype is with . 相似文献
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Concerning the obstacle-problem-like equation
, where + > 0 and – > 0, we give a complete characterization of all global two-phase solutions with quadratic growth both at 0 and infinity. 相似文献
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Juan Manfredi Arshak Petrosyan Henrik Shahgholian 《Calculus of Variations and Partial Differential Equations》2002,14(3):359-384
We consider a free boundary problem for the p-Laplacian
describing nonlinear potential flow past a convex profile K with prescribed pressure on the free stream line. The main purpose of this paper is to study the limit as of the classical solutions of the problem above, existing under certain convexity assumptions on a(x). We show, as one can expect, that the limit solves the corresponding potential flow problem for the -Laplacian
in a certain weak sense, strong enough however, to guarantee uniqueness. We show also that in the special case the limit is given by the distance function.
Received: 10 October 2000 / Accepted: 23 February 2001 / Published online: 19 October 2001 相似文献
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张辉 《应用泛函分析学报》2000,2(1):26-33
研究了方程-div(‖Du‖^-2Du)=λf(u)在R^n,n≥2中环域上的正的径向解的多重性。当f在正区域上有多个峰的情况下,我们获得了多个解。 相似文献
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Juan Luis Vazquez 《Monatshefte für Mathematik》2004,142(1-2):81-111
The paper contains a complete study of the large-time behavior of solutions of the Porous Medium Equation, ut = um with m > 1, posed in a bounded domain of the n-dimensional space with homogeneous boundary conditions. Asymptotic profiles are obtained and full proofs of the convergence results are given. Solutions with changing sign and problems posed in tubes are also considered. 相似文献