Research ArticleOpen AccessGoogle Scholar indexed
Existence Theory for Single Positive Solution to Fourth-Order Boundary Value Problems
School of Mathematics and Statistics, Northeast Petroleum University, Daqing, China
- 1 School of Mathematics and Statistics, Northeast Petroleum University, Daqing, China
Advances in Pure Mathematics·Volume 04 (2014)·Pages 480–486·Published 15 August 2014·DOI10.4236/apm.2014.48053
Copy link · social · email
Abstract
By fixed point theorem of a mixed monotone operator, we study boundary value problems to nonlinear singular fourth-order differential equations, and provide sufficient conditions for the existence and uniqueness of positive solution. The nonlinear term in the differential equation may be singular.
KeywordsMixed Monotone OperatorSingularExistenceUniqueness
- Jiang, D.Q., Liu, H. and Xu, X. (2005) Nonresonant Singular Fourth-Order Boundary Value Problems. Applied Mathematics Letters, 18, 69-75. http://dx.doi.org/10.1016/j.aml.2003.05.016
- Jiang, D.Q. (2000) Multiple Positive Solutions to Singular Boundary Value Problems for Superlinear Higher Order ODEs. Computers Mathematics with Applications, 40, 249-259. http://dx.doi.org/10.1016/S0898-1221(00)00158-9
- Liu, Y. (2003) Structure of a Class of Singular Boundary Value Problem with Superlinear Effect. Journal of Mathematical Analysis and Applications, 284, 64-75. http://dx.doi.org/10.1016/S0022-247X(03)00214-2
- Kong, L. and Wang, J. (2001) The Green’s Function for (k, n ? k) Conjugate Boundary Value Problems and Its Applications. Journal of Mathematical Analysis and Applications, 255, 404-422. http://dx.doi.org/10.1006/jmaa.2000.7158
- Zill, D.G. and Cullen, M.R. (2001) Differential Equations with Boundary-Value Problems. 5th Edition, Brooks Cole, Belmont.
- Liu, Y. (2004) Multiple Positive Solutions of Nonlinear Singular Boundary Value Problem for Fourth Order Equations. Applied Mathematics Letters, 17, 747-757. http://dx.doi.org/10.1016/j.aml.2004.06.001
- Guo, D. (2000) The Order Methods in Nonlinear Analysis. Shandong Technology and Science Press, Jinan.