共查询到20条相似文献,搜索用时 15 毫秒
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AbstractIn this paper, by the sub-super solution method we provide explicit lower bounds for the principal eigenvalue of the p-Laplacian on the unit ball. We compare our results with those of earlier studies and also demonstrate that they are in good agreement with numerical results. 相似文献
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The nonlinear eigenvalue problem for p-Laplacian is considered. We assume that 1 < p < N and that the function f is of subcritical growth with respect to the variable u. The existence and C1,α-regularity of the weak solution is proved. 相似文献
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Lin Feng Wang 《Annali di Matematica Pura ed Applicata》2012,191(3):539-550
Let M be an n-dimensional closed manifold with metric g, dμ = e h(x) dV(x) be the weighted measure and ? μ, p be the weighted p-Laplacian. In this article, we get the lower bound estimate of the first nonzero eigenvalue for the weighted p-Laplacian when the m-dimensional Bakry-émery curvature has a positive lower bound. 相似文献
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In this paper, we study the eigenvalue of p-Laplacian on finite graphs. Under generalized curvature dimensional condition, we obtain a lower bound of the first nonzero eigenvalue of p-Laplacian. Moreover, a upper bound of the largest p-Laplacian eigenvalue is derived. 相似文献
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In this paper, we consider a discrete four-point boundary value problem $$\triangle\bigl(\phi_p\bigl(\triangle u(k-1)\bigr)\bigr)+ \lambda e(k)f\bigl(u(k)\bigr)=0,\quad k\in N(1,T),$$ subject to boundary conditions $$\triangle u(0)-\alpha u(l_{1})=0,\qquad\triangle u(T)+\beta u(l_{2})=0,$$ by a simple application of a fixed point theorem. If e(k),f(u(k)) are nonnegative, the solutions of the above problem may not be nonnegative, this is the main difficulty for us to study positive solution of this problem. In this paper, we give restrictive conditions ??l 1??1, ??(T+1?l 2)??1 to guarantee the solutions of this problem are nonnegative, if it has, under the conditions e(k),f(u(k)) are nonnegative. We first construct a new operator equation which is equivalent to the problem and provide sufficient conditions for the nonexistence and existence of at least one or two positive solutions. In doing so, the usual restrictions $f_{0}=\lim_{u\rightarrow 0^{+}}\frac{f(u)}{\phi_{p}(u)}$ and $f_{\infty}=\lim_{u\rightarrow\infty}\frac{f(u)}{\phi_{p}(u)}$ exist are removed. 相似文献
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研究了一类具有非光滑局部Lipschitz位势(半变分不等式)的非线性特征值问题其中1
相似文献
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Mufa Chen 《数学学报(英文版)》2000,16(3):361-368
A variational formula for the lower bound of the principal eigenvalue of general Markov jump processes is presented. The result is complete in the sense that the condition is fulfilled and the resulting bound is sharp for Markov chains under some mild assumptions. Received November 15, 1999, Accepted March 9, 2000 相似文献
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《数学的实践与认识》2013,(22)
研究非齐次边界条件下,含有p-Laplacian算子的微分方程的可解性.应用Banach空间中的Krasnoselskii不动点定理,得到了边值问题正解的存在性结果. 相似文献
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We study the homogenization of p-Laplacian with obstacles in perforated domain, where the holes are periodically distributed and have random size. And we assume that the p-capacity of each hole is stationary ergodic. 相似文献
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Hua Su 《Journal of Applied Mathematics and Computing》2011,35(1-2):379-394
Let T be a time scale. The existence of positive solutions for the nonlinear four-point singular boundary value eigenvalue problem with higher-order p-Laplacian dynamic equations on time scales is studied. By using the fixed-point index theory, we derive an explicit interval of λ such that for any λ in this interval, the existence of at least one positive solution to the eigenvalue problem is guaranteed, and the existence of at least two solutions for λ in an appropriate interval is also discussed. 相似文献
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Harry Hochstadt 《Studies in Applied Mathematics》1972,51(1):99-105
The second order differential operator Lu = ?u″ + (M ? |x|)u defined on ( ?∞, ∞) is analyzed. It is shown that the pair of successive eigenvalues λ2n, λ2n+1 is asymptotically degenerate as M becomes large, for all n. 相似文献
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Let (M
n
, g) be a compact Riemannian manifold with convex boundary, let dμ = e
h(x)
dV (x) be a weighted measure on M, and let Δμ,p
be the corresponding weighted p-Laplacian on M. We obtain a lower bound for the first nonzero Neumann eigenvalue of Δμ,p
. 相似文献
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The leading asymptotic term for the function that counts theeigenvalues of the Stokes operator is determined for fairlygeneral underlying bounded domains. Moreover, the remainderis estimated in terms of the fractality of the boundary of thedomain. The results obtained resemble corresponding ones forthe Dirichlet Laplacian. 1991 Mathematics Subject Classification:35P20. 相似文献
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Kanhaiya Jha 《Numerical Functional Analysis & Optimization》2013,34(11):1146-1165
We investigate the minimization of the principal eigenvalue of the Laplacian under Neumann boundary conditions in case the weight has indefinite sign and varies in a class of rearrangements. Biologically, this minimization problem is motivated by the question of determining the most convenient spatial arrangement of favorable and unfavorable resources for a species to survive. The question may have practical importance in the context of reserve design. 相似文献