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POSITIVE SOLUTIONS OF A fourth order boundary value problem

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Applied Mathematics(A Journal of Chinese Universities) 2003年第2期18卷 138-142页

作者： Ren LishunDept. of Math., Zhoukou Teachers College, Henan 466000,China. Dept. of Math. Zhoukou Teachers College Henan China

The existence of positive solutions of the nonlinear fourth order problemu (4)(x)=λa(x)f(u(x)), u(0)=u′(0)=u′(1)=u(1)=0is studied, where a:[0,1]→R may change sign, f(0)>0,λ>0 is sufficiently small. Our appr... 详细信息

关键词： fourth-order boundary value problem positive solution Leray-Schauder fixed point theorem.

A NOTE ON UPPER AND LOWER SOLUTIONS METHOD FOR fourth-order boundary value problemS

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Annals of Differential Equations 2008年第1期24卷 117-120页

作者： Zhao Hong (School of Math.,Changchun Normal University,Changchun 130032)

In this paper,we deal with a class of boundary value *** give the existence of solution under the assumption that there exist lower and upper solutions to the *** result extends and complements the relevant ones which... 详细信息

关键词： fourth-order boundary value problem existence upper and lower solution method

Existence of Positive Solutions to fourth order Quasilinear boundary value problems

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Acta Mathematica Sinica,English Series 2006年第6期22卷 1825-1830页

作者： Zhan Bing BAI Wei Gao GE Institute of Mathematics Shandong University of Science and Technology Qingdao 266510 P.R. China Department of Applied Mathematics Beijing Institute of Technology Beijing 100081 P.R. China

In this paper, we generalize the fixed point theorem of cone expansion and compression of norm type to the theorem of functional type. As an application, the existence of positive solutions for some fourth-order beam equation boundary value problems is obtained. The emphasis is put on that the nonlinear term is dependent on all lower order derivatives.

关键词： fourth-order boundary value problem fixed point theorem positive solution

Existence of Multiple Positive Solutions for fourth order Two-point boundary value problems

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Northeastern Mathematical Journal 2002年第1期18卷 63-72页

作者：戚仕硕 Department of Mathematics Zhengzhou University Zhengzhou 450052

The present paper tackles two-point boundary value problems for fourth-order differential equations as follows:Several existence theorems on multiple positive solutions to the problems are obtained, and some examples ... 详细信息

关键词： existence theorem multiple positive solution fourth-order boundary value problem

MULTIPLE POSITIVE SOLUTIONS TO fourth-order SINGULAR boundary value problemS

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Annals of Differential Equations 2011年第1期27卷 9-12页

作者： Jinjun Fan(School of Mathematical Science,Shandong Normal University,Jinan 250014) Yinghua Yang(Primary School of South-North Temple,Zouping County,256200,Shandong)

In this paper,using the Krasnaselskii’s fixed point theory in cones and localization method,under more general conditions,the existence of n positive solutions to a class of fourth-order singular boundary value probl... 详细信息

关键词： fourth-order boundary value problem Krasnaselskii's fixed point theorem multiple positive solutions