一个典型弹性梁方程涉及第一特征值的正解
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摘要
运用锥理论和不动点指数方法,在与相应的线性算子第一特征值有关的条件下,获得了一个典型弹性梁方程正解的存在性,改进了相关文献的结论.
By cone theory and in the fixed point index method,the existence of positive solutions of a typical elastic beam equation has been obtained under the condition of the first eigenvalue of the corresponding linear operator,and the conclusions of relevant literatures been improved.
By cone theory and in the fixed point index method,the existence of positive solutions of a typical elastic beam equation has been obtained under the condition of the first eigenvalue of the corresponding linear operator,and the conclusions of relevant literatures been improved.
引文
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[10]CHAI G Q,HUANG C Y.Existence of Positive Solutions for the Fourth-Order Boundary Value Problem with the Coeffcient[J].J Acta Mathematics Scientia,2007,27A(6):1065-1073.
[11]CHEN T L.Existence of Positive Solutions for a Class of Fourth-Order Ordinary Differential Equations of Two-Point Boundary Value Problem[J].Chinese Journal of Engineering Mathematics,2010,27(4):679-683.
[12]姚庆六.两端简单支撑的奇异梁方程的正解[J].数学进展,2009,38(5):590-598.
[13]CUI Y J,SUN J X,ZOU Y M.Positive Solutions of Singular Boundary Value Problems of Fourth-Order Differential Equations[J].Journal of Mathematical Research&Exposition Mar,2009,29(2):376-380.
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[2] MA R Y,ZHANG J H,FU S M.The Method of Lower and Upper Solutions for Fourth-Order Two-Point Boundary Value Problems[J].Journal of Mathematical Analysis and Applications,1997,215(2):415-422.
[3] YAO Q.Positive Solutions for Eigenvalue Problems of Fourth-Order Elastic Beam Equations[J].Appl Math Lett,2004,17(2):237-243.
[4] YANG Y,ZHANG J.Existence of Solutions for Some Fourth-Order Boundary Value Problems with Parameters[J].Nonlinear Analysis.Theory,Methods&Applications,2008,69(4):1364-1375.
[5] LU H X,SUN L,SUN J X.Existence of Positive Solutions to a Non-Positive Elastic Beam Equation with Both Ends Fixed[J].Boundary Value Problems,2012,56(11):1-10.
[6]周韶林,吴红萍,韩晓玲.一类四阶三点边值问题正解的存在性[J].四川大学学报(自然科学版),2014,51(1):11-15.
[7] WEI Z L,ZHANG M C.Positive Solutions of Singular Sub-Linear Boundary Value Problems for Fourth-Order and Second-Order Differential Equation Systems[J],Applied Mathematics and Computation,2008,197(1):135-148.
[8] BONANNO G,BELLA B D,O’REGAN D.Non-Trivial Solutions for Nonlinear Fourth-Order Elastic Beam Equations[J].Comput Math Appl,2011,62(4):1862-1869.
[9] LI Y.Positive Solutions of Fourth-Order Boundary-Value Problem with Two Parameters[J].J Math Anal Appl,2003,281(2):477-484.
[10]CHAI G Q,HUANG C Y.Existence of Positive Solutions for the Fourth-Order Boundary Value Problem with the Coeffcient[J].J Acta Mathematics Scientia,2007,27A(6):1065-1073.
[11]CHEN T L.Existence of Positive Solutions for a Class of Fourth-Order Ordinary Differential Equations of Two-Point Boundary Value Problem[J].Chinese Journal of Engineering Mathematics,2010,27(4):679-683.
[12]姚庆六.两端简单支撑的奇异梁方程的正解[J].数学进展,2009,38(5):590-598.
[13]CUI Y J,SUN J X,ZOU Y M.Positive Solutions of Singular Boundary Value Problems of Fourth-Order Differential Equations[J].Journal of Mathematical Research&Exposition Mar,2009,29(2):376-380.
[14]孙经先.非线性泛函分析及其应用[M].北京:科学出版社,2008.
[15]郭大钧,孙经先.非线性积分方程[M].济南:山东科学技术出版社,1987.