Existence and Uniqueness of Positive Solution for 2mth-Order Nonlinear Differential Equation with Boundary Conditions

Abstract

In this paper, we study the existence and uniqueness of positive solution for 2mth-order nonlinear differential equation with boundary conditions, by using the fixed point theorems on compression and expansion of cones.

Share and Cite:

Liu, J. (2015) Existence and Uniqueness of Positive Solution for 2mth-Order Nonlinear Differential Equation with Boundary Conditions. Journal of Applied Mathematics and Physics, 3, 1178-1185. doi: 10.4236/jamp.2015.39145.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Zhang, S.Q. (2010) A Class Nonlinear Boundary Value Problem for Third-order Differential Equation with Singular Perturbation. Journal of Sanming University, 27, 106-108.
[2] Liu, Y. (2007) Two-point Boundary Value Problems for n-Order Nonlinear Differential Equation. Journal of Shenyang Institute of Aeronautical Engineering, 24, 95-96.
[3] He, J.H., Hu, L. and Wang, L.L. (2007) Positive Solutions of BVPs for a System of Even-Order ODEs. Journal of Anhui University Natural Science Edition, 31, 1-4.
[4] Lin, H.F. (2013) Existence and Uniqueness of Solutions for Boundary Value Problems of Nonlinear Differential Equations. Master’s Thesis, Qufu Normal University, Qufu.
[5] Kong, L.B. and Wang, J.Y. (2001) The Green’s Function of (k, n - k) Conjugate Boundary Value Problem and Its Applications. Journal of Mathematical Analysis and Applications, 255, 404-422.
http://dx.doi.org/10.1006/jmaa.2000.7158
[6] Li, S.J., Liao, F.F. and Zhu, H.L. (2014) Multiplicity of Positive Solutions to Second-Order Singular Differential Equations with a Parameter. Boundary Value Problems, 1, 1-12.
http://dx.doi.org/10.1186/1687-2770-2014-115

Copyright © 2021 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.