共查询到20条相似文献,搜索用时 0 毫秒
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On the basis of some new Liouville theorems, under suitableconditions, a priori estimates are obtained of positive solutionsof the problem
where RN (N 2) is a bounded smooth domain, p>1 and isa parameter, , q are given constants such that p1<<p*1, <q, p*=Np/(Np) if N > p and p*= when N p, and a(x) is a continuous nonnegative function. Makinguse of the LeraySchauder degree of a compact mappingand a priori estimates, the paper finds that the problem abovepossesses at least one positive solution. It also discussesthe corresponding perturbed problem, where a(x) is replacedby a(x)+, >0. The results are strikingly different from thoseobtained for the case =p1. 相似文献
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Mathematical Notes - 相似文献
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一类拟线性椭圆型偏微分方程的先验界的估计 总被引:1,自引:0,他引:1
近几年对边值问题-div(|Du|p-2Du)=λf(u)}在Ω上u|(?)Ω=0正解方面已经得到了许多结果.这里λ>0,Ω是有界区域和对s≥0,f(s)≥0.在本文中在条件N≥p>1,Ω=B1={x∈RN,|x|<1}和f∈C1(0,∞)∩C0([0,∞)),f(0)=0,研究了这类问题的正对称解的先验界估计. 相似文献
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Huashui ZHAN 《数学年刊B辑(英文版)》2011,32(3):397-416
By an interpolation method, an intrinsic Harnack estimate and some supestimates are established for nonnegative solutions to a general singular parabolic equation. 相似文献
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一类具有高阶转向点的二次问题的奇摄动 总被引:3,自引:0,他引:3
研究带有高阶转向点的二阶非线性微分方程的边值问题εy″=f(t)y′2+g(t,y)y(a,ε)=A,y(b,ε)=B的奇异摄动现象.在一定的条件下,得到了摄动解关于退化解的渐近性质及误差估计. 相似文献
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We obtain a priori bounds for the solutions of master Markov quantum equations in the Heisenberg and Schrödinger pictures. 相似文献
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Joseph Gruendler 《Transactions of the American Mathematical Society》1998,350(9):3797-3814
Ordinary differential equations are considered which contain a singular perturbation. It is assumed that when the perturbation parameter is zero, the equation has a hyperbolic equilibrium and homoclinic solution. No restriction is placed on the dimension of the phase space or on the dimension of intersection of the stable and unstable manifolds. A bifurcation function is established which determines nonzero values of the perturbation parameter for which the homoclinic solution persists. It is further shown that when the vector field is periodic and a transversality condition is satisfied, the homoclinic solution to the perturbed equation produces a transverse homoclinic orbit in the period map. The techniques used are those of exponential dichotomies, Lyapunov-Schmidt reduction and scales of Banach spaces. A much simplified version of this latter theory is developed suitable for the present case. This work generalizes some recent results of Battelli and Palmer.
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We study the approximation of a multiscale reaction–diffusion system posed on both macroscopic and microscopic space scales. The coupling between the scales is done through micro–macro flux conditions. Our target system has a typical structure for reaction–diffusion flow problems in media with distributed microstructures (also called, double porosity materials). Besides ensuring basic estimates for the convergence of two-scale semi-discrete Galerkin approximations, we provide a set of a priori feedback estimates and a local feedback error estimator that help in designing a distributed-high-errors strategy to allow for a computationally e?cient zooming in and out from microscopic structures. The error control on the feedback estimates relies on two-scale-energy, regularity, and interpolation estimates as well as on a fine bookeeping of the sources responsible with the propagation of the (multiscale) approximation errors. The working technique based on a priori feedback estimates is in principle applicable to a large class of systems of PDEs with dual structure admitting strong solutions. 相似文献
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The author applies the two-variable expansion procedure to anon-linear problem in singular perturbations, and compares theresults with those obtained using the composite expansion method. 相似文献
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The author applies the two-variable expansion procedure to anexample in singular perturbations and shows how the validityof this procedure can be established in many cases (includingsome non-linear problems). 相似文献
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A Priori Estimates and Existence of Positive Solutions to Quasilinear Elliptic Equations in General Form 下载免费PDF全文
Wang Xujia 《偏微分方程(英文版)》1992,5(4)
In this paper we prove the existence of a positive solution to the following superlinear elliptic Dirichlet problem, - Σ^n_{i,j=1}aij(x, u, Du)D_{ij}u = f(x, u, Du) in Ω, \quad u = 0 on ∂Ω where f satisfies certain growth conditions. 相似文献
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Differential Equations - We consider the linear differential pencil $$A(\lambda )\equiv L-\lambda V $$ , where $$L\equiv -y^{\prime {}\prime }+q(x)y$$ is the Sturm–Liouville operator with... 相似文献