Fully nonlinear fourth-order equations with functional boundary conditions. (English) Zbl 1138.34008

Cabada, A.; Minhós, F. M.

J. Math. Anal. Appl. 340, No. 1, 239-251 (2008).

The authors prove an existence and location result for a nonlinear fourth-order ordinary differential equation with functional boundary conditions. The approach relies on the method of upper-lower solutions and the use of Schauder’s fixed point theorem. An application to a human spine deformation model is also included.

Reviewer: Sergiu Aizicovici (Athens/Ohio)

MSC:

34B15	Nonlinear boundary value problems for ordinary differential equations
34C60	Qualitative investigation and simulation of ordinary differential equation models

Keywords:

fourth-order functional problems; Nagumo-type condition; lower and upper solutions; fixed-point theory; beam equation; human spine continuous model

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