Existence Theory for Single Positive Solution to Fourth-Order Boundary Value Problems
Author(s)
Ying He*
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.
Cite this paper
He, Y. (2014) Existence Theory for Single Positive Solution to Fourth-Order Boundary Value Problems. Advances in Pure Mathematics, 4, 480-486. doi: 10.4236/apm.2014.48053.
He, Y. (2014) Existence Theory for Single Positive Solution to Fourth-Order Boundary Value Problems. Advances in Pure Mathematics, 4, 480-486. doi: 10.4236/apm.2014.48053.
References
[1] 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 [2] 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 [3] 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 [4] 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 [5] Zill, D.G. and Cullen, M.R. (2001) Differential Equations with Boundary-Value Problems. 5th Edition, Brooks Cole, Belmont. [6] 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 [7] Guo, D. (2000) The Order Methods in Nonlinear Analysis. Shandong Technology and Science Press, Jinan.
[1] 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 [2] 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 [3] 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 [4] 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 [5] Zill, D.G. and Cullen, M.R. (2001) Differential Equations with Boundary-Value Problems. 5th Edition, Brooks Cole, Belmont. [6] 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 [7] Guo, D. (2000) The Order Methods in Nonlinear Analysis. Shandong Technology and Science Press, Jinan.