近年来,非线性临界增长椭圆方程得到了广泛的研究.对于半线性方程,许多正则性结果已经得到.本文我们考虑拟线性方程-sum from i=sum from i=1 to N （?）/（（?）<sub>x</sub><sub>i</sub>）（α<sub>i&l...近年来,非线性临界增长椭圆方程得到了广泛的研究.对于半线性方程,许多正则性结果已经得到.本文我们考虑拟线性方程-sum from i=sum from i=1 to N （?）/（（?）<sub>x</sub><sub>i</sub>）（α<sub>i</sub>（x,u,▽u））=α（x,u,▽u）,x∈（?）（?）R<sup>N</sup> （1）的 W<sup>（?）,p</sup>（?）弱解的正则性.假定α<sub>i</sub>（x,z,q）,α（x,z,q）是（?）×R×R<sup>N</sup> 上的 Carathéodory 函数。展开更多
The authors study the existence of solutions for the nonlinear elliptic system {-Mλ＋,（D2u）=f（u,v）in Ω,-Mλ＋,（D2u）=g（u,v）inΩ,u≥0,v≥0 inΩ,u=v=0 on Ω, where Ω is a bounded convex domain in RN, N ≥ 2. I...The authors study the existence of solutions for the nonlinear elliptic system {-Mλ＋,（D2u）=f（u,v）in Ω,-Mλ＋,（D2u）=g（u,v）inΩ,u≥0,v≥0 inΩ,u=v=0 on Ω, where Ω is a bounded convex domain in RN, N ≥ 2. It is shown that under some assumptions on f and g, the problem has at least one positive solution （u, v）.展开更多
In this paper,we are concerned with the regularity and symmetry of positive solutions of the following nonlinear integral system u（x） = ∫R n G α（x-y）v（y） q/｜y｜β dy,v（x） = ∫R n G α（x-y）u（y） p/｜y｜β...In this paper,we are concerned with the regularity and symmetry of positive solutions of the following nonlinear integral system u（x） = ∫R n G α（x-y）v（y） q/｜y｜β dy,v（x） = ∫R n G α（x-y）u（y） p/｜y｜β dy for x ∈ R n,where G α（x） is the kernel of Bessel potential of order α,0 ≤β 〈 α 〈 n,1 〈 p,q 〈 n-β/β and 1/p ＋ 1 ＋ 1/q ＋ 1 〉 n-α ＋ β/n.We show that positive solution pairs（u,v） ∈ L p ＋1（R n） × L q ＋1（R n） are Ho¨lder continuous,radially symmetric and strictly decreasing about the origin.展开更多
This paper obtain C-1,C-alpha- regularity of weak solutions to the p-Laplacian obstacle problem with C-1,C-beta-obstacle function under controllable growth conditions.
In this article, the authors investigate the existence problem for Hardy Henon type strongly indefinite elliptic systems. Existence results are obtained for such systems with superlinear subcritical nonlinearities.
In this article, we consider the existence of positive solutions for weakly coupled nonlinear elliptic systems {-△u＋u=（1＋a（x））｜u｜P-1u＋μ｜u｜a-2u｜v｜β＋λv in Rn,-△u＋u=（1＋b（x））｜v｜p-1v＋μ｜u｜a｜...In this article, we consider the existence of positive solutions for weakly coupled nonlinear elliptic systems {-△u＋u=（1＋a（x））｜u｜P-1u＋μ｜u｜a-2u｜v｜β＋λv in Rn,-△u＋u=（1＋b（x））｜v｜p-1v＋μ｜u｜a｜v｜β-2v＋λu in Rn To find nontrivial solutions, we first investigate autonomous systems. In this case, results of bifurcation from semi-trivial solutions are obtained by the implicit function theorem. Next, the existence of positive solutions of problem （0.1） is obtained by variational methods.展开更多
文摘近年来,非线性临界增长椭圆方程得到了广泛的研究.对于半线性方程,许多正则性结果已经得到.本文我们考虑拟线性方程-sum from i=sum from i=1 to N （?）/（（?）<sub>x</sub><sub>i</sub>）（α<sub>i</sub>（x,u,▽u））=α（x,u,▽u）,x∈（?）（?）R<sup>N</sup> （1）的 W<sup>（?）,p</sup>（?）弱解的正则性.假定α<sub>i</sub>（x,z,q）,α（x,z,q）是（?）×R×R<sup>N</sup> 上的 Carathéodory 函数。
基金supported by National Natural Sciences Foundations of China (10571175,10631030)
文摘The authors study the existence of solutions for the nonlinear elliptic system {-Mλ＋,（D2u）=f（u,v）in Ω,-Mλ＋,（D2u）=g（u,v）inΩ,u≥0,v≥0 inΩ,u=v=0 on Ω, where Ω is a bounded convex domain in RN, N ≥ 2. It is shown that under some assumptions on f and g, the problem has at least one positive solution （u, v）.
基金Chen research is supported by NSF of China (10961015)Yang research is supported by NSF of China (10961016)the GAN PO555 Program of Jiangxi
文摘In this paper,we are concerned with the regularity and symmetry of positive solutions of the following nonlinear integral system u（x） = ∫R n G α（x-y）v（y） q/｜y｜β dy,v（x） = ∫R n G α（x-y）u（y） p/｜y｜β dy for x ∈ R n,where G α（x） is the kernel of Bessel potential of order α,0 ≤β 〈 α 〈 n,1 〈 p,q 〈 n-β/β and 1/p ＋ 1 ＋ 1/q ＋ 1 〉 n-α ＋ β/n.We show that positive solution pairs（u,v） ∈ L p ＋1（R n） × L q ＋1（R n） are Ho¨lder continuous,radially symmetric and strictly decreasing about the origin.
文摘This paper obtain C-1,C-alpha- regularity of weak solutions to the p-Laplacian obstacle problem with C-1,C-beta-obstacle function under controllable growth conditions.
文摘In this article, the authors investigate the existence problem for Hardy Henon type strongly indefinite elliptic systems. Existence results are obtained for such systems with superlinear subcritical nonlinearities.
基金supported by National Natural Science Foundations of China(10631030,10961016)
文摘In this article, we consider the existence of positive solutions for weakly coupled nonlinear elliptic systems {-△u＋u=（1＋a（x））｜u｜P-1u＋μ｜u｜a-2u｜v｜β＋λv in Rn,-△u＋u=（1＋b（x））｜v｜p-1v＋μ｜u｜a｜v｜β-2v＋λu in Rn To find nontrivial solutions, we first investigate autonomous systems. In this case, results of bifurcation from semi-trivial solutions are obtained by the implicit function theorem. Next, the existence of positive solutions of problem （0.1） is obtained by variational methods.
