In order to study three-point BVPs for fourth-order impulsive differential equation of the form with the following boundary conditions u'(0) = u(1) = 0. u'(0) == 0 = u'(1) -φq(α)u'(η). the authors t...In order to study three-point BVPs for fourth-order impulsive differential equation of the form with the following boundary conditions u'(0) = u(1) = 0. u'(0) == 0 = u'(1) -φq(α)u'(η). the authors translate the fourth-order impulsive differential equations with p-Laplacian (*) into three-point BVPs for second-order differential equation without impulses and two-point BVPs for second-order impulsive differential equation by a variable transform. Based on it, existence theorems of positive solutions for the boundary value problems (*) are obtained.展开更多
This paper proves that the first eigenfunctions of the Finsler p-Lapalcian are C^(1,α). Using a gradient comparison theorem and one-dimensional model, we obtain the sharp lower bound of the first Neumann and closed e...This paper proves that the first eigenfunctions of the Finsler p-Lapalcian are C^(1,α). Using a gradient comparison theorem and one-dimensional model, we obtain the sharp lower bound of the first Neumann and closed eigenvalue of the p-Laplacian on a compact Finsler manifold with nonnegative weighted Ricci curvature,on which a lower bound of the first Dirichlet eigenvalue of the p-Laplacian is also obtained.展开更多
基金supported by the National Natural Science Foundation of China(11101349,11071205)the Natural Science Foundation of Jiangsu Province(BK2011042)+1 种基金the NSF of the Education Department of Jiangsu Province(11KJB110013)Jiangsu Province postgraduate training project
基金Supported by NSFC(No.11801426)Natural Science Basic Research Plan in Shaanxi Province of China(No.2017JQ1022)Scientific Research Program of Shaanxi Higher Education Institutions(No.12JK0868)。
基金Supported by by National Natural Science Foundation of China(11071053)the Natural Science Foundation of Hebei Province(A2010001482)the Key Project of Science and Research of Hebei Education Department(ZH2012080)
基金Supported by the National Natural Foundation of China (10371006)the Youth Teachers Science Projects of Central University for Nationalities (No.A08).
文摘In order to study three-point BVPs for fourth-order impulsive differential equation of the form with the following boundary conditions u'(0) = u(1) = 0. u'(0) == 0 = u'(1) -φq(α)u'(η). the authors translate the fourth-order impulsive differential equations with p-Laplacian (*) into three-point BVPs for second-order differential equation without impulses and two-point BVPs for second-order impulsive differential equation by a variable transform. Based on it, existence theorems of positive solutions for the boundary value problems (*) are obtained.
基金supported by National Natural Science Foundation of China (Grant No. 11471246)Natural Science Foundation of Higher Education in Anhui Province (Grant No. KJ2014A257)
文摘This paper proves that the first eigenfunctions of the Finsler p-Lapalcian are C^(1,α). Using a gradient comparison theorem and one-dimensional model, we obtain the sharp lower bound of the first Neumann and closed eigenvalue of the p-Laplacian on a compact Finsler manifold with nonnegative weighted Ricci curvature,on which a lower bound of the first Dirichlet eigenvalue of the p-Laplacian is also obtained.
