共查询到20条相似文献,搜索用时 56 毫秒
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杨芬 《数学物理学报(A辑)》2015,(2):282-287
研究如下非齐次双调和方程-△~2u+u~p+f(x)=0,x∈R~n(*)正解的存在性,其中△~2是双调和算子,p1,n≥5,f≠0.在文献[16[的基础上,得到:对f给定条件,方程(*)有一类不同于文献[16]的两种衰减的正解. 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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本文研究Rn(n≥ 3)上的半线性椭圆方程 -Δu=f(u)的C2 正解 .如果f(u)在 ( 0 ,∞ )上局部有界并且对某个α 1 <α相似文献
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本文讨论了Rn 上如下一类带临界增长的拟线性椭圆方程正解的存在性 :-div(| u|p- 2 u) -axn| u|p- 2 u xn +|u|p- 2u=up - 1 ,xn ≠ 0 ,x∈Rn.这里 ,1
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带导数项的非齐次边值问题正解的存在性 总被引:1,自引:0,他引:1
李和成 《应用泛函分析学报》2002,4(2):181-184
运用Schauder不动点定理讨论了带导数项的非齐次边值问题:u"+a(t)f(t,u,u')=0,00.正解的存在性.其中:f关于u是超线性增长的. 相似文献
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本文用非线性分析中的临界点理论和Strauss引理讨论了半线性椭圆方程-△u a(r)u=b(r)u^p g(r,u)在R^n中的径向正解的存在性,其中p=n 2/n-2,n≥3。 相似文献
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研究了n阶中立型方程(x(t)-cx(t-τ)^(n)+p(t)x(g(t))=0,t≥t0,n≥1(*)正解的存在性,在p(t)常号和变号的情况下,给出了(*)存在衰减正解的充分条件,特别,这偏离 文「2」,「4-6」和「8-12」的有关结果。 相似文献
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本文考虑如下带有Sobolev临界指标项的非齐次椭圆方程{-?u=λu+|u|~(2*)-~2u+f,x∈?,u=0,x∈??,这里2~*=2N/N-2是Sobolev临界指标,N≥3,??R~N是一个有界开区域.0≤λλ_1,这里λ_1是算子-?的第一个特征值,并且假设f∈H_0~1(?)~(-1),当f满足适当的条件时,此方程在H_0~1(?)中至少具有两个解u_0和u_1.而且,当f≥0时,u_0≥0和u_1≥0. 相似文献
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陈振韬 《高校应用数学学报(英文版)》1994,9(3):231-236
In this paper we study a class of degenerate nonlinear elliptic systems with homogeneous Dirichlet boundary conditions by the monotone iteration method. The existence and uniqueness of the positive solution of such a system are proved. In particular conditions which ensure that the iteration process converges to the unique solution are given. 相似文献
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In this paper, the existence of positive solutions for a class of quasilinear elliptic differential equation systems are established by Schauder-TychonofF fixed point theorem. 相似文献
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In this paper, the authors study the existence and nonexistence of multiple positive solutions for problem(*)μwhere h ∈ H-1(RN), N ≥ 3, |f(x,u)| ≤ C1up-1 + C2u with C1 > 0, C2∈ [0,1) being some constants and 2 < p < ∞. Under some assumptions on f and h, they prove that there exists a positive constant μ* <∞ such that problem (*)μ has at least one positive solution uμ if μ,∈ (0,μ*), there are no solutions for (*)μ if μ, > μ* and uμ is increasing with respect to μ∈ (0,μ*); furthermore, problem (*)μ has at least two positive solution for μ ∈ (0,μ*) and a unique positive solution for μ, =μ* if p ≤2N/N-2. 相似文献
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In this paper, we prove the existence of at least one positive solution pairto the following semilinear elliptic systemby using a linking theorem, where K(x)is a positive function in L^s(R^N) for some s 〉 1and the nonnegative functions f, g ∈ C(R, R) are of quasicritical growth, superlinear atinfinity. We do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual. Our main result can be viewed as a partial extension of a recent result of Alves, Souto and Montenegro in [1] concerning the existence of a positive solution to the following semilinear elliptic problemand a recent result of Li and Wang in [22] concerning the existence of nontrivial solutions to a semilinear elliptic system of Hamiltonian type in R^N. 相似文献
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1.APrioriBounds##DTherearealotofresultsfortheprioriboundsandtheexistenceofpositivesolutionsofsemilinearellipticequations(see[2],[3]).Weshallinvestigatetheprioriboundsandtheexistenceofpositivesolutionsforsystemofellipticboundaryvalueproblems:Wealwaysassume… 相似文献
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Zhang Hui Guo Zongm ing Dept. ofMath. Henan Norm alUniv. Xinxiang . Institute ofSystem s Science Academ ia Sinica Beijing . 《高校应用数学学报(英文版)》1999,(3)
§1 IntroductionInthispaperwecontinuetoconsidertheexistenceofpositiveradialsolutionsforthequasilinearellipticequation-div(|Du|p-2Du)=f(u) inΩ,(1)u(x)=0 onΩ,wherex∈Rn,n≥2,Ω={x:a<|x|<b,a,b>0},andp>1,f∈C1((0,∞))∩C0([0,∞))satisfyingthefollowinghypotheses… 相似文献
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1 IntroductionIn this paper we consider the following quasilinear elliptic problemwhere -- A. 'u = --div(l V ulp--' 7 u), A 2 0 is a real parametcr, 0 < m < p -- 1 < q < oc. flis a bounded domain in RN(N 2 3).During the last decade HLaplaJce equatiolls have e11jOyed a growing attention. After theinitial works of Poliozeav[1], and of Brezis and Nirenberg[2], there has been great number ofcontributious to the study of that kind of problem (1.1)A(see [3-161). Recently, equationiuvolving th… 相似文献
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研究如下N维奇异半线性椭圆方程△u+f(x,u)=0, x∈RN(N≥3),其中函数f:RN× R+→R+连续,在u=0有奇异性;采用上-下解方法给出该方程具有满足如下性质的有界正整体解u的条件: u∈C2+θloc(RN)使得lim |x|→∞ u(x)=0且u(x)≥εmin{1,|x|2-N},其中ε>0是常数;并证明:若条件添加"f关于u单调不增"的限制,则这种解是唯一的. 相似文献