The upper and lower solution method for a class of singular nonlinear second order three-point boundary value problems

In this paper we develop the upper and lower solution method and the monotone iterative technique for a class of singular nonlinear second order three-point boundary value problems. A maximum principle is established and some new existence results are obtained.

[1]  E. Zeidler.  Nonlinear functional analysis and its applications , 1988 .

[2]  Wenying Feng,et al.  On an M -point boundary value problem , 1997 .

[3]  C. P. Gupta.  A Note on a Second Order Three-Point Boundary Value Problem , 1994 .

[4]  Wenying Feng,et al.  Solvability of three point boundary value problems at resonance , 1997 .

[5]  C. P. Gupta,et al.  Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation , 1992 .

[6]  Eberhard Zeidler.  The Schauder Fixed-Point Theorem and Compactness , 1986 .

[7]  Chia-Ven Pao,et al.  Nonlinear parabolic and elliptic equations , 1993 .

[8]  R. Ma,et al.  Positive solutions of a nonlinear three-point boundary-value problem. , 1999 .

[9]  C. P. Gupta.  A second order m -point boundary value problem at resonance , 1995 .

[10]  J.‐Y. Wang,et al.  On the Existence of Positive Solutions to a Three‐Point Boundary Value Problem for the One‐Dimensional p‐Laplacian , 1997 .

[11]  C. P. Gupta,et al.  A Sharper Condition for the Solvability of a Three-Point Second Order Boundary Value Problem , 1997 .

[12]  Sotiris K. Ntouyas,et al.  On an m -point boundary-value problem for second-order ordinary differential equations , 1994 .

[13]  V. Lakshmikantham,et al.  Monotone iterative techniques for nonlinear differential equations , 1985 .

[14]  Sotiris K. Ntouyas,et al.  Solvability of an m-Point Boundary Value Problem for Second Order Ordinary Differential Equations , 1995 .