CLC number: O175.8
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 0000-00-00
Cited: 4
Clicked: 4907
YAO Qing-liu. Existence of solutions and positive solutions to a fourth-order two-point BVP with second derivative[J]. Journal of Zhejiang University Science A, 2004, 5(3): 353-357.
@article{title="Existence of solutions and positive solutions to a fourth-order two-point BVP with second derivative",
author="YAO Qing-liu",
journal="Journal of Zhejiang University Science A",
volume="5",
number="3",
pages="353-357",
year="2004",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2004.0353"
}
%0 Journal Article
%T Existence of solutions and positive solutions to a fourth-order two-point BVP with second derivative
%A YAO Qing-liu
%J Journal of Zhejiang University SCIENCE A
%V 5
%N 3
%P 353-357
%@ 1869-1951
%D 2004
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2004.0353
TY - JOUR
T1 - Existence of solutions and positive solutions to a fourth-order two-point BVP with second derivative
A1 - YAO Qing-liu
J0 - Journal of Zhejiang University Science A
VL - 5
IS - 3
SP - 353
EP - 357
%@ 1869-1951
Y1 - 2004
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2004.0353
Abstract: Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the “height” of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends.
[1] Aftabizadeh, A.R., 1986. Existence and uniqueness theorems for fourth-order boundary value problems.J. Math. Anal. Appl.,116:415-426.
[2] Del Peno, M.A., Manasevich, R.F., 1991. Existence for a fourth-order boundary value problem under a two-parameter nonresonance condition.Proc. Amer. Math. Soc.,112:81-86.
[3] Ma, R., Zhang, J., Fu, S., 1997. The method of lower and upper solutions for fourth-order two-point boundary value problems.J. Math. Anal. Appl.,215:415-422.
[4] Usmani, R.A., 1979. A uniqueness theorem for a boundary value problem.Proc. Amer. Math. Soc.,77:327-335.
[5] Yang, Y., 1988. Fourth-order two-point boundary value problems.Proc. Amer. Math. Soc.,104:175-180.
[6] Yao, Q., Bai, Z., 1999. Existence of positive solutions of BVP foru(4)(t)-λh(t)f(u(t))=0.Chinese Annals of Math.,20A:575-578(in Chinese).
[7] Yao, Q., 2002. Existence and multiplicity of positive solutions for a class of second-order three-point nonlinear boundary value problems.Acta Math. Sinica, 46:1057-1064 (in Chinese).
[8] Yao, Q., 2003. The existence and multiplicity of positive solutions for a third-order three-point boundary value problem.Acta Math. Appl. Sinica, English Ser., 19:117-122.
Open peer comments: Debate/Discuss/Question/Opinion
<1>