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1.
This article investigates fourth-order singular p-Laplacian boundary value problems (BVPs), and obtains the necessary and sufficient conditions for existence of positive solutions for fourth-order singular p-Laplacian BVPs on closed interval.  相似文献   

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We prove some existence results for the Webster scalar curvature problem on the Heisenberg group and on the unit sphere of n+1, under the assumption of some natural symmetries of the prescribed curvatures. We use variational and perturbation techniques. Mathematics Subject Classification (2000) 35J20, 35H20, 35J60, 43A80  相似文献   

3.
We prove an invariant Harnack’s inequality for operators in non-divergence form structured on Heisenberg vector fields when the coe?cient matrix is uniformly positive definite, continuous, and symplectic. The method consists in constructing appropriate barriers to obtain pointwise-to-measure estimates for supersolutions in small balls, and then invoking the axiomatic approach developed by Di Fazio, Gutiérrez, and Lanconelli to obtain Harnack’s inequality.  相似文献   

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CLC Number:  相似文献   

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In the present paper, we aim to investigate the existence of solutions for the quasilinear boundary value problem involving fractional operators in the ψ-fractional space H([0, T],R) with asymmetric nonlinearities.  相似文献   

6.
王月山 《数学学报》2006,49(3):709-720
本文得到了一类具有小BMO系数的非散度型椭圆方程解的局部W2,p(p≥2) 正则性结果,并给出了这个结果的一个应用.  相似文献   

7.
研究了一类具多偏差变元的n-维p-Laplacian方程周期解的存在性,利用迭合度理论得到了存在周期解的新条件.  相似文献   

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本文研究了一类具偏差变元的二阶n-维p-Laplacian方程调和解的存在性,在对阻尼项不作限制的前提下,利用拓扑度理论得到了存在调和解的新条件,改进了一些已有的结果.  相似文献   

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Fourth-order advanced differential equations naturally appear in models concerning physical, biological, chemical phenomena applications. The aim of this paper is to study the oscillatory properties of fourth-order advanced differential equations with p-Laplacian like operators. We obtain some oscillation criteria for the equation by the theory of comparison. The obtained results improve the well-known oscillation results in the literature. Some examples to illustrate the results are given.  相似文献   

10.
In this note we consider the blow-up rate of solutions for p-Laplacian equation with nonlinear source, ut = div(|↓△u|p-2↓△u)+uq, (x, t) ∈ RN × (0, T), N ≥ 1. When q 〉 p - 1, the blow-up rate of solutions is studied.  相似文献   

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By employing Mawhin's continuation theorem, the existence of solution for a p-Laplacian equation with nonlinear boundary conditions is obtained under simple assumptions.  相似文献   

13.
Asymptotic behavior of the solutions of the p-Laplacian equation   总被引:1,自引:0,他引:1  
The asymptotic behavior of the solutions for p-Laplacian equations as p→∞ is studied.  相似文献   

14.
本文将研究一般区域上高维p-Laplacian方程保号解的存在性:{u(x)=0,x∈ЭΩ,-div(φp(■u))=a(x)φp(u++β(x)φp(u-)+ra(x)f(u)),x∈Ω,其中Ω是RN中一个有界且在其边界上光滑的区域,N≥2,1p-2s,a(x)∈C(Ω,(0,+∞)),u+=max{u,0},u-=-min{u,0},a{x},β(x)∈C(Ω);f∈C(R,R)对于s>0,sf(s)>0成立.当f0■(0,∞)或f∞∈(0,∞)(其中f0=|s|→0limf(s)/φp(s),f∞=|s|→+∞limf(s)/φp(s)),且r≠0属于一定区间时,可以获得上述高维p-Laplacian方程保号解的存在性.我们用全局分歧技巧和连通序列集取极限的方法获得主要结果.  相似文献   

15.
本文将研究一般区域上高维p-Laplacian方程保号解的存在性:{u(x)=0,x∈ЭΩ,-div(φp(■u))=a(x)φp(u++β(x)φp(u-)+ra(x)f(u)),x∈Ω,其中Ω是RN中一个有界且在其边界上光滑的区域,N≥2,1p-2s,a(x)∈C(Ω,(0,+∞)),u+=max{u,0},u-=-min{u,0},a{x},β(x)∈C(Ω);f∈C(R,R)对于s>0,sf(s)>0成立.当f0■(0,∞)或f∞∈(0,∞)(其中f0=|s|→0limf(s)/φp(s),f∞=|s|→+∞limf(s)/φp(s)),且r≠0属于一定区间时,可以获得上述高维p-Laplacian方程保号解的存在性.我们用全局分歧技巧和连通序列集取极限的方法获得主要结果.  相似文献   

16.
宋常修 《数学季刊》2007,22(4):475-481
In this paper,the author studies the boundary value problems for a p-Laplacian functional difference equation.By using a fixed point theorem in cones,sufficient conditions are established for the existence of the positive solutions.  相似文献   

17.
In this paper, we study a nonlinear Dirichlet boundary value problem for difference equations involving the p-Laplacian with two positive parameters. One result on the existence of at least three solutions for this problem is obtained using critical point theory.  相似文献   

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By making full use of the estimates of solutions to nonstationary Stokes equations and the method discussing global stability, we establish the global existence theorem of strong solutions for Navier-Stokes equatios in arbitrary three dimensional domain with uniformlyC 3 boundary, under the assumption that |a| L 2(Θ) + |f| L 1(0,∞;L 2(Θ)) or |∇a| L 2(Θ) + |f| L 2(0,∞;L 2(Θ)) small or viscosityv large. Herea is a given initial velocity andf is the external force. This improves on the previous results. Moreover, the solvability of the case with nonhomogeneous boundary conditions is also discussed. This work is supported by foundation of Institute of Mathematics, Academia Sinica  相似文献   

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