Journal of Applied Mathematics

Existence of Solutions of Nonlinear Mixed Two-Point Boundary Value Problems for Third-Order Nonlinear Differential Equation

Yongxin Gao and Fengqin Wang

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Abstract

The authors use the upper and lower solution method to study the existence of solutions of nonlinear mixed two-point boundary value problems for third-order nonlinear differential equation    y ′′′ = f ( x , y , y , y ′′ ) ,    y ( b ) = h ( y ( a ) ) ,    p ( y ( a ) , y ( b ) , y ( a ) , y ( b ) ) = 0 ,    g ( y ( a ) , y ( b ) , y ( a ) , y ( b ) , y ′′ ( a ) , y ′′ ( b ) ) = 0 . Some new existence results are obtained by developing the upper and lower solution method. Some applications are also presented.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 262139, 12 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495234

Digital Object Identifier
doi:10.1155/2012/262139

Mathematical Reviews number (MathSciNet)
MR2956522

Zentralblatt MATH identifier
1255.34023

Citation

Gao, Yongxin; Wang, Fengqin. Existence of Solutions of Nonlinear Mixed Two-Point Boundary Value Problems for Third-Order Nonlinear Differential Equation. J. Appl. Math. 2012 (2012), Article ID 262139, 12 pages. doi:10.1155/2012/262139. https://projecteuclid.org/euclid.jam/1355495234


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