## On fourth order boundary value problems arising in beam analysis.(English)Zbl 0715.34032

Summary: We consider a general fourth order nonlinear ordinary differential equation together with two point boundary conditions which occur in the deflection of a beam rigidly fastened at left and simply fastened at right. For this general boundary value problem, we provide necessary and sufficient conditions for the existence and uniqueness of the solutions. We also obtain upper estimates on the length of interval so that Newton’s method converges quadratically to the unique solutions. Some of our results are the best possible in their frame.

### MSC:

 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 65L10 Numerical solution of boundary value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 74K10 Rods (beams, columns, shafts, arches, rings, etc.)

### Keywords:

two point boundary conditions; Newton’s method