In this paper we consider the existence of infinitely many positive solutions for second order nonlinear eigenvalue problem with singular coefficient function. By the use of Krasnosel'skii fixed point theorem of c...In this paper we consider the existence of infinitely many positive solutions for second order nonlinear eigenvalue problem with singular coefficient function. By the use of Krasnosel'skii fixed point theorem of cone expansion-compression type we give several sufficient conditions.展开更多
Let G be a simple connected graph with order n.Let L(G)and Q(G)be the normalized Laplacian and normalized signless Laplacian matrices of G,respectively.Letλk(G)be the k-th smallest normalized Laplacian eigenvalue of ...Let G be a simple connected graph with order n.Let L(G)and Q(G)be the normalized Laplacian and normalized signless Laplacian matrices of G,respectively.Letλk(G)be the k-th smallest normalized Laplacian eigenvalue of G.Denote byρ(A)the spectral radius of the matrix A.In this paper,we study the behaviors ofλ2(G)andρ(L(G))when the graph is perturbed by three operations.We also study the properties ofρ(L(G))and X for the connected bipartite graphs,where X is a unit eigenvector of L(G)corresponding toρ(L(G)).Meanwhile we characterize all the simple connected graphs withρ(L(G))=ρ(Q(G)).展开更多
In this paper,a residual type of a posteriori error estimator for the general second order elliptic eigenpair approximation by the mixed finite element method is derived and analyzed,based on a type of superconvergenc...In this paper,a residual type of a posteriori error estimator for the general second order elliptic eigenpair approximation by the mixed finite element method is derived and analyzed,based on a type of superconvergence result of the eigenfunction approximation.Its efficiency and reliability are proved by both theoretical analysis and numerical experiments.展开更多
文摘In this paper we consider the existence of infinitely many positive solutions for second order nonlinear eigenvalue problem with singular coefficient function. By the use of Krasnosel'skii fixed point theorem of cone expansion-compression type we give several sufficient conditions.
基金by the National Natural Science Foundation of China(No.11871398)the Natural Science Basic Research Plan in Shaanxi Province of China(Program No.2018JM1032)the Fundamental Research Funds for the Central Universities(No.3102019ghjd003).
文摘Let G be a simple connected graph with order n.Let L(G)and Q(G)be the normalized Laplacian and normalized signless Laplacian matrices of G,respectively.Letλk(G)be the k-th smallest normalized Laplacian eigenvalue of G.Denote byρ(A)the spectral radius of the matrix A.In this paper,we study the behaviors ofλ2(G)andρ(L(G))when the graph is perturbed by three operations.We also study the properties ofρ(L(G))and X for the connected bipartite graphs,where X is a unit eigenvector of L(G)corresponding toρ(L(G)).Meanwhile we characterize all the simple connected graphs withρ(L(G))=ρ(Q(G)).
基金supported by National Natural Science Foundation of China(Grant Nos.11001259,11031006,11071265,11201501 and 91230110)National Basic Research Program of China(973 Project)(Grant No. 2011CB309703)+3 种基金International S&T Cooperation Program of China(Grant No. 2010DFR00700)Croucher Foundation of Hong Kong Baptist Universitythe National Center for Mathematics and Interdisciplinary Science,CAS,the President Foundation of AMSS-CASthe Fundamental Research Funds for the CentralUniversities(Grant No. 2012121003)
文摘In this paper,a residual type of a posteriori error estimator for the general second order elliptic eigenpair approximation by the mixed finite element method is derived and analyzed,based on a type of superconvergence result of the eigenfunction approximation.Its efficiency and reliability are proved by both theoretical analysis and numerical experiments.
