EXISTENCE OF POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEM FOR ONE-DIMENSIONAL p-LAPLACIAN

EXISTENCE OF POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEM FOR ONE-DIMENSIONAL p-LAPLACIAN

导出

摘要 We study the existence of positive solutions to boundary value problems for one- dimensional p-Laplacian under some conditions about the first eigenvalues correspon- ding to the relevant operators by the fixed point theory. The main difficulties are the computation of fixed point index and the subadditivity for positively 1-homogeneous operator. We study the existence of positive solutions to boundary value problems for one- dimensional p-Laplacian under some conditions about the first eigenvalues correspon- ding to the relevant operators by the fixed point theory. The main difficulties are the computation of fixed point index and the subadditivity for positively 1-homogeneous operator.

作者 Yujun Cui Shu Zhang

机构地区 Dept.of Math.

出处《Annals of Differential Equations》 2014年第2期137-143,共7页 微分方程年刊（英文版）

基金 supported by the National Natural Science Foundation of China(11371221,11071141) the Specialized Research Foundation for the Doctoral Program of Higher Educationof China(20123705110001) the Program for Scientific Research Innovation Team in Colleges and Universities of Shandong Province and Foundation of SDUST

关键词 P-LAPLACIAN boundary value problem first eigenvalue fixed point theory p-Laplacian boundary value problem first eigenvalue fixed point theory

分类号 O175 [理学—基础数学]

引文网络
相关文献

参考文献16

1R.P. Agarwal, G. Akrivis, Boundary value problems occurring in plate deflection theory, J. Comp. Appl. Math., 8(1982),145-154.
2R.P. Agarwal, H. Lii, D. O'Regan, Eigenvalues and the one-dimensional p-Laplacian, J. Math. Anal. Appl., 266(2002),383-400.
3C. De Coster, Pairs of positive solutions for the one-dimensional p-Laplacian, Nonlinear Ana- lysis, 23(1994),669-681.
4Y. Cui, J. Sun, A generalization of Mahadevan's version of the Krein-Rutman theorem and lications to p-Laplacian boundary value problems, Abstract and Applied Analysis, Volume 12, Article ID 305279, 14 pages.
5M.D. Pino, M. Elgueta, R. Mamasevich, A homotopic deformation along p of a Leray-Schauder degree result and existence for (|u'|P-2u')' + f(t, u) = 0, u(0) = u(T) = 0, p > 1, J. Differential Equations, 80(1989),1-13.
6M. Gacia-Huidobro, R. Manásevich, F. Zanolin, Strongly nonlinear second-order ODEs with rapidly growing terms, J. Math. Anal. Appl., 202(1996),1-26.
7J. Garcia-Melian, J.S. de Lis, Maximum and comparison principles for operator involving the p-Laplacian, J. Math. Anal. Appl., 218(1998),49-64.
8N.B. Huy, T.D. Thanh, On an eigenvalue problem involving the one-dimensional p-Laplacian, J. Math. Anal. Appl., 290(2004),123-131.
9L. Kong, J. Wang, Multiple positive solutions for the one-dimensional p-Laplacian, Nonlinear Analysis, 42(2000),1327-1333.
10R. Mahadevan, A note on a non-linear Krein-Rutman theorem, Nonlinear Analysis, 67(2007), 3084-3090.

1Qing Liu YAO.Existence,Multiplicity and Infinite Solvability of Positive Solutions for One-Dimensional p-Laplacian[J].Acta Mathematica Sinica,English Series,2005,21(4):691-698. 被引量：12
2Zhiyu Zhang (Dept. of Math., Taiyuan Institute of Technology, Taiyuan 030008) Youfeng Zhang (Yuncheng Middle School, Yuncheng 044000, Shanxi) Fengqin Zhang (Dept. of Math., Yuncheng University, Yuncheng 044000, Shanxi).MULTIPLICITY OF POSITIVE SOLUTIONS TO MULTIPOINT BOUNDARY VALUE PROBLEM WITH ONE-DIMENSIONAL p-LAPLACIAN[J].Annals of Differential Equations,2010,26(4):484-493. 被引量：4
3De-xiang Ma,Wei-gao Ge,Xue-gang Chen.Positive Solution of Multi-Point Boundary Value Problems for the One-Dimensional p-Laplacian with Singularities[J].Acta Mathematicae Applicatae Sinica,2005,21(4):661-670. 被引量：1
4Shen Chunfang,Yang Liu,Liu Xiping.SOLVABILITY FOR m-POINT BOUNDARY VALUE PROBLEM AT RESONANCE WITH ONE-DIMENSIONAL p-LAPLACIAN[J].Annals of Differential Equations,2007,23(2):188-198.
5Wang Feng, Zhang Fang (School of Math. and Physics, Jiangsu Polytechnic University, Changzhou 213164, Jiangsu) Liu Chunhan (Dept. of Math., Shandong Education College, Jinan 250013).MULTIPLE POSITIVE SOLUTIONS TO A SYSTEM OF NONLINEAR HAMMERSTEIN TYPE INTEGRAL EQUATIONS[J].Annals of Differential Equations,2009,25(1):62-66.
6缪烨红,张吉慧.Positive solutions of three-point boundary value problems[J].Applied Mathematics and Mechanics(English Edition),2008,29(6):817-823. 被引量：1
7Zeng Xianwu,Du Nailin,Chen Shihua.On Reduced Variational Equations of Coupled Systems[J].Wuhan University Journal of Natural Sciences,1997,2(2):21-25. 被引量：3
8晏平,章梅荣.Best Estimates of Weighted Eigenvalues of One-dimensional p-Laplacian[J].Northeastern Mathematical Journal,2003,19(1):39-50.
9Weihua Jiang,Zhihong Chen(College of Sciences,Hebei University of Science and Technology,Shijiazhuang 050018,Linu Zhou(College of Math.and Information Science,Hebei Normal University,Shijiazhuang 050018).POSITIVE SOLUTIONS TO(k,n-k) NONHOMOGENEOUS BOUNDARYVALUE PROBLEM[J].Annals of Differential Equations,2012,28(3):269-275.
10晏平,章梅荣.Periodic Eigenvalues of One-Dimensional p-Laplacian with Indefinite Weights[J].Tsinghua Science and Technology,2003,8(5):533-536.

Annals of Differential Equations

2014年第2期

浏览历史

内容加载中请稍等...

EXISTENCE OF POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEM FOR ONE-DIMENSIONAL p-LAPLACIAN

参考文献16

相关作者

相关机构

相关主题

浏览历史