Construction of upper and lower solutions with applications to singular boundary value problems


An upper and lower solution theory is presented for the Dirichlet boundary value problem \(y^{\prime\prime}+f(t,y,y^{\prime})=0\), \(0<t <1\) with \(y(0)=y(1)=0\). Our nonlinearity may be singular in its dependent variable and is allowed to change sign.


R.P. Agarwal

D. O’Regan

Radu Precup
Babes-Bolyai University, Cluj-Napoca, Romania



Paper coordinates

R.P. Agarwal, D.O. Regan, R. Precup, Construction of upper and lower solutions with applications to singular boundary value problems,  J. Comput. Anal. Appl. 7 (2005), 205-221.


About this paper


J. Comput. Anal. Appl.

Publisher Name


Print ISSN
Online ISSN

MR2223477, Zbl 1085.34016

google scholar link

[1] R.P. Agrawal, D.O’Regan and V. Lakshmikantham, An upper and lower solution approach for nonlinear singular boundary value problems with y’ dependence, Archives of Inequalities and Applicaitons 1(2003), 119-135.
[2] R.P. Agarwal, D.O’Regan, V. Lakshmikantham and S. Leela, an upper and lower solution theory for singular Emden-Fowler equations, Nonlinear Analysis: Real World Applications, 3(2002), 275-291.
[3] A. Callegari and A. Nachman, Some singular nonlinear differential equaitons arising in boundary layer theory, J. Math. Anal. Appl., 64(1978), 96-105.
[4] J.A. Gatica, V. Oliker and P. Waltman, Singular nonlinear boundary value problems for second order differential equations, J. Differential Equations, 79(1989), 62-78.
[5] H. Lu, D.O’Regan and C. Zhong, Existence of positive solutions for the singular equation (φ_{p}(y′))′+g(t,y,y′)=0, Nonlinear Oscillations, to appear.
[6] C.D.Luning and W.L.Perry, Positive solutions of negative exponent generalized Emden-Fowler boundary value problems, SIAM J. Math. Anal., 12(1981), 874-879.
[7] D.O’Regan, Theory of singular boundary value problems, World Scientific, Singapore, 1994.
[8] D.O’Regan and R.P. Agarwal, Singular problems: an upper and lower solution approach, J. Math. Anal. Appl., 251(2000), 230-250.


Related Posts