共查询到16条相似文献,搜索用时 78 毫秒
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主要研究全空间上一类带权函数的积分方程组正解的径向对称性和单调性问题.在合适条件下,主要利用积分形式的移动平面方法,Hardy—Littlewwood—Sobolev(HLS)和Holder不等式给出了积分方程组正解的径向对称性和单调性的结论.这一结论很好的推广了已有的结果. 相似文献
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该文讨论了扇型区域上一类半线性椭圆型方程组混合边值问题正解的对称性和单调性.所得结果是文献[1]-[14]的一个推广. 相似文献
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通过结合移动平面法及其角点区域的Hopf引理得到了有界区域上一类完全非线性椭圆型方程组解的对称性和单调性. 相似文献
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该文运用移动平面法研究了一类混合局部-非局部半线性椭圆方程奇异解的单调性和对称性. 相似文献
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本文研究在有界域和无界域上含Hardy-Leray势的分数阶p-Laplacian方程,运用移动平面法,得到该方程正解的单调性和对称性,并将带Hardy-Leray势的分数阶方程解的对称性结果推广到更一般的分数阶p-Laplacian方程. 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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我们在穿孔单位球上研究下面多重调和Dirichlet问题{(-Δ)ku=f(u),在B\{0)内,u>0,在B\{0)内,u=(e)u/(e)v=…=(e)k-1u/(e)vk-1=0,在(e)B上,其中,B是RN中的单位球,v是(e)B的单位外法向量,N>2k,k≥2.在f满足适当假设条件下,如果0是不可去奇点,我们... 相似文献
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利用时标理论中的Nabla积分建立了含参数Nabla积分比■以及变限含参数Nabla积分比■的单调性法则.在含参数Nabla积分比部分中,还详细研究了一些特殊情形,包括时标下的多项式之比以及Nabla拉普拉斯变换之比.利用这些单调性法则,证明了函数■的单调性,其中■分别为第一类和第二类修正的贝塞尔函数,Ju(s):=(s/2)-uIu(s)和yu(s):=Ku(s)-K0(s). 相似文献
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In this paper, we study the positive solutions for a class of integral systems and prove that all the solutions are radially symmetric and monotonically decreasing about some point. Moreover, we also obtain the uniqueness result for a special case. We use a new type of moving plane method introduced by Chen-Li-Ou [1]. Our new ingredient is the use of Hardy-Littlewood-Sobolev inequality instead of Maximum Principle. 相似文献
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In this paper we study radial symmetry and monotonicity of positive solutions of an integral equation arising from some higher-order semilinear elliptic equations in the whole space Rn. Instead of the usual method of moving planes, we use a new Hardy-Littlewood-Sobolev (HLS) type inequality for the Bessel potentials to establish the radial symmetry and monotonicity results. 相似文献
13.
The authors establish a general monotonicity formula for the following elliptic system
△ui+fi(x,ui,…,um)=0 in Ω,
where Ω belong to belong to R^n is a regular domain, (fi(x, u1,... ,um)) = △↓F(x,→↑u), F(x,→↑u ) is a given smooth function of x ∈ R^n and →↑u = (u1,…,um) ∈ R^m. The system comes from understanding the stationary case of Ginzburg-Landau model. A new monotonicity formula is also set up for the following parabolic system
δtui-△ui-fi(x,ui,…,um)=0 in(ti,t2)×R^n,
where t1 〈 t2 are two constants, (fi(x,→↑u ) is given as above. The new monotonicity formulae are focused more attention on the monotonicity of nonlinear terms. The new point of the results is that an index β is introduced to measure the monotonicity of the nonlinear terms in the problems. The index β in the study of monotonieity formulae is useful in understanding the behavior of blow-up sequences of solutions. Another new feature is that the previous monotonicity formulae are extended to nonhomogeneous nonlinearities. As applications, the Ginzburg-Landau model and some different generalizations to the free boundary problems are studied. 相似文献
△ui+fi(x,ui,…,um)=0 in Ω,
where Ω belong to belong to R^n is a regular domain, (fi(x, u1,... ,um)) = △↓F(x,→↑u), F(x,→↑u ) is a given smooth function of x ∈ R^n and →↑u = (u1,…,um) ∈ R^m. The system comes from understanding the stationary case of Ginzburg-Landau model. A new monotonicity formula is also set up for the following parabolic system
δtui-△ui-fi(x,ui,…,um)=0 in(ti,t2)×R^n,
where t1 〈 t2 are two constants, (fi(x,→↑u ) is given as above. The new monotonicity formulae are focused more attention on the monotonicity of nonlinear terms. The new point of the results is that an index β is introduced to measure the monotonicity of the nonlinear terms in the problems. The index β in the study of monotonieity formulae is useful in understanding the behavior of blow-up sequences of solutions. Another new feature is that the previous monotonicity formulae are extended to nonhomogeneous nonlinearities. As applications, the Ginzburg-Landau model and some different generalizations to the free boundary problems are studied. 相似文献
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In this paper,we are interested in the existence of positive solutions for the Kirchhoff type problems{-(a_1 + b_1M_1(∫_?|▽u|~pdx))△_(_pu) = λf(u,v),in ?,-(a_2 + b_2M_2(∫?|▽v|~qdx))△_(_qv) = λg(u,v),in ?,u = v = 0,on ??,where 1 p,q N,M i:R_0~+→ R~+(i = 1,2) are continuous and increasing functions.λ is a parameter,f,g ∈ C~1((0,∞) ×(0,∞)) × C([0,∞) × [0,∞)) are monotone functions such that f_s,f_t,g_s,g_t ≥ 0,and f(0,0) 0,g(0,0) 0(semipositone).Our proof is based on the sub-and super-solutions techniques. 相似文献
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本文研究如下形式的半线性椭圆方程组:-Δu = f1(v), -Δv = f2(u),x∈Rn(n≥3).假设在(0,∞)上fi(i =1,2)是一个正的严格增函数并且fi(s)s-n 2n-2 是非增的,本文得到了该方程组正解的精确形式. 相似文献