Existence of solutions for a fully nonlinear fourth-order two-point boundary value problem

被引：9

作者：

Pei M. ^{[1
]}

Chang S.K. ^{[2
]}

机构：

[1] Department of Mathematics, Beihua University

[2] Department of Mathematics, Yeungnam University

来源：

Journal of Applied Mathematics and Computing | 2011年 / 37卷 / 1-2期

关键词：

Boundary value problem; Existence; Leray-Schauder degree theory; Nagumo condition;

D O I：

10.1007/s12190-010-0434-3

中图分类号：

学科分类号：

摘要：

In this paper, we investigate the existence of solutions of a fully nonlinear fourth-order differential equation x(4)=f(t,x,x′, x″,x″′, [t∈[0,1 with one of the following sets of boundary value conditions; x′(0)=x(1)=a0x″(0)-b 0x″′(0)=a1x″(1)+b 1x″′(1)=0, x(0)=x″(1)=a0x″(0)- b0x″′(0)=a1x″(1)+b 1x″′(1)=0 By using the Leray-Schauder degree theory, the existence of solutions for the above boundary value problems are obtained. Meanwhile, as an application of our results, an example is given. © 2010 Korean Society for Computational and Applied Mathematics.

引用

页码：287 / 295

页数：8

共 24 条

[1]

Aftabizadeh A.R., Existence and uniqueness theorems for fourth-order boundary value problems, J. Math. Anal. Appl., 116, pp. 415-426, (1986)

[2]

Agarwal R.P., Chow Y.M., Iterative methods for a fourth order boundary value problem, J. Comput. Appl. Math., 10, pp. 203-217, (1984)

[3]

Bai Z., The upper and lower solution method for some fourth-order boundary value problems, Nonlinear Analysis, Theory, Methods and Applications, 67, 6, pp. 1704-1709, (2007)

[4]

Cabada A., The method of lower and upper solutions for second, third, fourth and higher order boundary value problems, J. Math. Anal. Appl., 185, pp. 302-320, (1994)

[5]

Cabada A., Angel Cid J., Sanchez L., Positivity and lower and upper solutions for fourth order boundary value problems, Nonlinear Analysis, Theory, Methods and Applications, 67, 5, pp. 1599-1612, (2007)

[6]

Del Pino M.A., Manasevich R.F., Existence for a fourth-order boundary value problem under a two parameter nonresonance condition, Proc. Am. Math. Soc., 112, pp. 81-86, (1991)

[7]

Ehme J., Eloe P.W., Henderson J., Upper and lower solution methods for fully nonlinear boundary value problems, J. Differ. Equ., 180, pp. 51-64, (2001)

[8]

Franco D., O'Regan D., Peran J., Fourth-order problems with nonlinear boundary conditions, Journal of Computational and Applied Mathematics, 174, 2, pp. 315-327, (2005)

[9]

Feng H., Ji D., Ge W., Existence and uniqueness of solutions for a fourth-order boundary value problem, Nonlinear Anal., 70, pp. 3561-3566, (2009)

[10]

Graef J.R., Kong L., A necessary and sufficient condition for existence of positive solutions of nonlinear boundary value problems, Nonlinear Analysis, Theory, Methods and Applications, 66, 11, pp. 2389-2412, (2007)

← 1 2 3 →