A monotone method for constructing extremal solutions to fourth-order periodic boundary value problems

In this paper we describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problemu^(^4^)(t)=f(t,u(t),u''(t)),[email protected]?[0,[email protected]],u(0)=u([email protected]),u^'(0)=u^'([email protected]),u''(0)=u''([email protected]),u^@?(0)=u^@?([email protected])in the presence of an upper solution @b and a lower solution @a with @b=<@a.

[1]  Extremal solutions of second order nonlinear periodic boundary value problems , 1990 .

[2]  J. Nieto,et al.  A generalized upper and lower solutions method for nonlinear second order ordinary differential equations. , 1992 .

[3]  Juan J. Nieto,et al.  Periodic boundary value problems for nonlinear higher order ordinary differential equations , 1992 .

[4]  Alberto Cabada,et al.  Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions , 1993 .

[5]  D. Jiang,et al.  A generalized periodic boundary value problem for the one-dimensional p-Laplacian , 1997 .

[6]  Yong Yang.  Fourth-order two-point boundary value problems , 1988 .

[7]  Johann Schröder.  Fourth order two-point boundary value problems; estimates by two-sided bounds , 1984 .

[8]  C. P. Gupta,et al.  Existence and uniqueness theorems for the bending of an elastic beam equation , 1988 .

[9]  Irena Rachůnková,et al.  Upper and lower solutions satisfying the inverse inequality , 1997 .

[10]  Riaz A. Usmani.  A uniqueness theorem for a boundary value problem , 1979 .

[11]  Alberto Cabada,et al.  A generalization of the monotone iterative technique for nonlinear second order periodic boundary value problems , 1990 .

[12]  Pierpaolo Omari.  A monotone method for constructing extremal solutions of second order scalar boundary value problems , 1986 .

[13]  Zhang Jihui,et al.  The Method of Lower and Upper Solutions for Fourth-Order Two-Point Boundary Value Problems , 1997 .

[14]  C. P. Gupta,et al.  Existence and uniqueness theorems for some fourth order fully quasilinear boundary value problems , 1990 .

[15]  A. R. Aftabizadeh.  Existence and uniqueness theorems for fourth-order boundary value problems , 1986 .

[16]  Junyu Wang,et al.  On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions , 1995 .

[17]  P. Omari.  Non-ordered lower and upper solutions and solvability of the periodic problem for the Liénard and the Rayleigh equations , 1988 .

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

[19]  Juan J. Nieto,et al.  Nonlinear second-order periodic boundary value problems , 1988 .

[20]  Alberto Cabada,et al.  The Method of Lower and Upper Solutions for Second, Third, Fourth, and Higher Order Boundary Value Problems , 1994 .

[21]  P. Omari,et al.  Remarks on the lower and upper solutions method for second- and third-order periodic boundary value problems , 1992 .

[22]  C. P. Gupta,et al.  Existence and uniqueness results for the bending of an elastic beam equation at resonance , 1988 .

[23]  Chengwen Wang.  Generalized upper and lower solution method for the forced Duffing equation , 1997 .

[24]  Nonlinear second order periodic value problems with caratheodory functions , 1989 .