Solvability of some fourth (and higher) order singular boundary value problems

Abstract Existence results for a variety of singular fourth order boundary value problems of the form yiv = f(t, y, y′, y″) are given. Here our nonlinear term f may be singular at t = 0, t = 1, y = 0, and/or y″ = 0. For example, some singularities of the type y−a and ¦y″¦ −b are included. Also we discuss and treat the extension of these results to nth order boundary value problems.

[1]  Donal O'Regan,et al.  Existence and nonexistence for a singular boundary value problem , 1988 .

[2]  Ronald B. Guenther,et al.  Nonlinear boundary value problems for ordinary differential equations , 1985 .

[3]  Steven D. Taliaferro,et al.  A nonlinear singular boundary value problem , 1979 .

[4]  L. Jackson.  BOUNDARY VALUE PROBLEMS FOR LIPSCHITZ EQUATIONS , 1980 .

[5]  D. O’Regan,et al.  Existence of solutions to some singular initial value problems , 1988 .

[6]  Daniel O'regan,et al.  Topological transversality: Applications to third order boundary value problems , 1987 .

[7]  L. Jackson.  Existence and uniqueness of solutions of boundary value problems for Lipschitz equations , 1979 .

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

[9]  J. Henderson,et al.  Nonlinear Boundary Value Problems and a Priori Bounds on Solutions , 1984 .

[10]  C. D. Luning,et al.  Positive Solutions of Negative Exponent Generalized Emden–Fowler Boundary Value Problems , 1981 .

[11]  A. Granas,et al.  Nonlinear boundary value problems for some classes of ordinary differential equations , 1980 .

[12]  L. Bobisud.  Existence and behavior of positive solutions for a class of parabolic reaction-diffusion equations , 1988 .

[13]  Donal O'Regan,et al.  Fourth (and higher) order singular boundary value problems , 1990 .

[14]  J. Baxley.  Nonlinear Two Point Boundary Value Problems , 1968 .

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