应用数学学报
首页  |  期刊介绍  |  编 委 会  |  投稿指南  |  期刊订阅  |  广告服务  |  相关链接  |  下载中心  |  联系我们  |  留言板
 
应用数学学报 英文版  
   
   
高级检索 »  
应用数学学报  2011, Vol. 34 Issue (5): 801-812    DOI:
论文 最新目录 | 下期目录 | 过刊浏览 | 高级检索  |   
带P-Laplacian 算子的四点四阶奇异边值问题的对称正解
栾世霞1, 赵艳玲2
1. 曲阜师范大学数学科学学院, 曲阜 273165;
2. 定陶县职业教育中心, 定陶 274100
Symmetric Positive Solutions of Fourth-order Four-point Boundary Value Problems with P-Laplacian Operator
LUAN Shixia1, ZHAO Yanling2
1. School of Mathematical Sciences, Qufu Normal University, Qufu 273165;
2. Dingtao County Vocational Education Center, Dingtao 274100
 全文: PDF (280 KB)   HTML (1 KB)   输出: BibTeX | EndNote (RIS)      背景资料
摘要 本文主要利用上下解方法和Schauder不动点定理, 在更广泛的条件下研究了一类带P-Laplacian 算子的四点四阶奇异边值问题的对称正解的存在性. 克服了对非线性微分算子[φp(u″)]″ Fredholm抉择定理和极大值原理不能使用的困难, 改进并推广了最近的一些已知结果.  
服务
把本文推荐给朋友
加入我的书架
加入引用管理器
E-mail Alert
RSS
作者相关文章
关键词P-Laplacian算子   奇异边值问题   上下解   对称正解   Schauder不动点定理     
Abstract: This paper is concerned with the fourth-order singular BPVs. Under a general assumption, the existence of symmetric positive solution are obtained by the method of upper-lower solutions and Schauder's fixed point theorem. Fredholm alternative theorem and minimax theorems are invalid here and our results generalize many recent studies.  
Key wordsP-Laplacian operator   singular boundary value problem   lower and upper solutions   symmetric positive solution   Schauder's fixed point theorem   
收稿日期: 2009-01-10;
基金资助:

山东省自然科学基金(ZR2009AL016)资助项目.

引用本文:   
. 带P-Laplacian 算子的四点四阶奇异边值问题的对称正解[J]. 应用数学学报, 2011, 34(5): 801-812.
. Symmetric Positive Solutions of Fourth-order Four-point Boundary Value Problems with P-Laplacian Operator[J]. Acta Mathematicae Applicatae Sinica, 2011, 34(5): 801-812.
 
[1] Bernis F. Compactness of the Support in Convex and Nonvex four order Elasticity Problem. Nonl.Anal., 1982, 6: 1221-1243
[2] Zill D G, Cullen M R. Differential Equations with Boundary-Value Problems. (fifth ed.), Brooks/Cole,2001
[3] Timoshenko S P. Theory of Elastic Stability. New York: McGraw-Hill, 1961
[4] Soedel W. Vibrations of Shells and Plates. New York: Dekker, 1993
[5] Chen S H, Ni W, Wang C P. Positive Solution of order Ordinary Differtial Equation with Four-pointBoundary Conditions. Appl. Math. Lett., 2006, 19: 191-168
[6] Graef J R, Qian C, Yang B. A Three Point Boundary Value Problem for Nonlinear Fourth orderDifferential Equations. J. Math. Anal. Appl., 2003, 287: 217-233
[7] Ma R Y, Zhang J H, Fu S M. The Methord of Lower and Upper Solutions for Fourth-order Two-pointBoundary Value Problem. Anal. Appl., 1997, 215: 415-422
[8] Liu B. Positive Solutions of Fourth-order Two-point Boundary Value Problem. Appl. Math. Comp.,2004, 148: 407-420
[9] Liu L S, Zhang X G, Wu Y H. Positive Solutions of Fourth-order Nonlinear Singular Sturm-LiouvilleEigenvalue Problems. J. Math. Anal. Appl., 2007, 326: 1212-1224
[10] Agarwal R. On Fourth-order Boundary Value Porblems Arising in Beam Analysis. Diff. Inte. Equa.,1989, 148: 91-110
[11] Cabada A. The Method of Lower and Upper Solutions for Second, Third, Fourth, and Higher orderBoundary Value Problems. J. Math. Anal. Appl., 1994, 185: 302-320
[12] De Coster C, Sanchez L. Upper and Lower Solutions, Ambrosetti-Prodi Problem and Positive Solutionsfor Fourth order O.D.E. Riv, Math. Pura. Appl., 1994 14: 1129-1136
[13] Dunninger D. Existence of Positive Solutions for Fourth-order Nonlinear Problems. Boll. UnioneMath. Ital., 1987, 7: 1129-1138
[14] Korman P. A Maximum Principle for Fourth-order Ordinary Differential Equations. Appl. Anal.,1989, 33: 267-273
[15] Sadyrbaev F. Two-point Boundary Value Problem for Fourth-order. Acta. Univ. Latv., 1990, 553:84-91
[16] Schroder J. Fourth-order Two-point Boundary Value Problems: Estimates by Two Side Bounds.Nonl. Anal., 1984, 8: 107-114
[17] Ma R Y. On the Existence of Positive Solutiong of Fourth-order Ordinary Differential Equations.Alle. Anal., 1995, 59: 225-231
[18] Usmami R A. A Uniqueness Theorem for a Boundary Value Problem. Proc. Amer. Math. Soc.,1979, 59: 327-335
[19] Gulta C P. Existence and Uniqueness Results for the Bending of an Elastic Beam Equation at Reso-nance. J. Math. Anal. Appl., 1988, 135: 208-225
[20] Lian H R, Wang P G,Ge W G. Unbounded Upper and Lower Solutions Method for Sturm-LiouvilleBoundary Value Problem on Infinite Intervals. Nonl. Anal., 2009, 70: 2627-2633
[1] 赵书芬, 张建元. 时滞脉冲抛物型微分方程解的存在性及其在种群动力学中的应用[J]. 应用数学学报, 2011, 34(6): 1068-1081.
[2] 夏静, 余志先, 袁荣. 一类具有非局部扩散的时滞Lotka-Volterra竞争模型的行波解[J]. 应用数学学报, 2011, 34(6): 1082-1093.
[3] 张红侠, 刘立山, 郝新安. 具有积分边界条件的四阶奇异特征值问题的正解[J]. 应用数学学报, 2011, 34(5): 873-885.
[4] 张兴秋. 奇异四阶积分边值问题正解的存在唯一性[J]. 应用数学学报, 2010, 33(1): 38-50.
[5] 孙 彦, 刘立山. 三阶奇异边值问题的正解[J]. 应用数学学报, 2009, 32(1): 50-59.
[6] 田元生. 三阶$p$-Laplacian方程三点奇异边值问题三个正解的存在性[J]. 应用数学学报, 2008, 31(6): 1118-1127.
[7] 黄建华, 黄立宏. 高维格上时滞反应扩散方程的行波解[J]. 应用数学学报, 2005, 28(1): 100-113.
[8] 付一平. 一类凝血系统的周期解[J]. 应用数学学报, 2004, 27(4): 638-645.
[9] Feng Qin ZHANG, Zhi En MA, Ju Rang YAN. 一阶带参数的时滞微分方程的边值问题[J]. 应用数学学报, 2003, 26(3): 525-532.
[10] 钟金标, 陈祖墀. 一类拟线性方程组的可解性[J]. 应用数学学报, 2003, 26(3): 420-426.
[11] 李翠哲, 葛渭高. p-Laplacian奇异半正单调问题的非负解[J]. 应用数学学报, 2003, 26(3): 434-442.
[12] 程建纲. 二阶微分方程边值问题的多重正解[J]. 应用数学学报, 2003, 26(2): 272-279.
[13] 刘颖. n阶非线性常微分方程两点及三点边值问题解的存在性的进一步结果[J]. 应用数学学报, 2003, 26(1): 72-90.
[14] 史永东. 半导体物理中的一个两点边值问题[J]. 应用数学学报, 2002, 25(1): 36-42.
[15] 陈芳启. Banach空间中非线性二阶积分微分方程初值问题的极(值)解[J]. 应用数学学报, 2001, 17(3): 289-295.
  版权所有 © 2009 应用数学学报编辑部   E-mail: amas@amt.ac.cn
京ICP备05002806号-9