Positive solutions for higher order ordinary differential equations. (English) Zbl 0814.34017

Eloe, Paul W.; Henderson, Johnny

Electron. J. Differ. Equ. 1995, No. 03, 8 p. (1995).

Summary: Solutions that are positive with respect to a cone are obtained for the boundary value problem \(u^{(n)}+ a(t) f(u)= 0\), \(u^{(i)}(0)= u^{(n- 2)}(1)= 0\), \(0\leq i\leq n- 2\), in the cases that \(f\) is either superlinear or sublinear. The methods involve application of a fixed point theorem for operators on a cone.

MSC:

34B15

Nonlinear boundary value problems for ordinary differential equations

Keywords:

positive solutions; boundary value problem