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On the existence of positive solutions of fourth-order ordinary differential equations. (English) Zbl 0841.34019

We study the existence of positive solutions of the equations \[ {d^4 y\over dx^4}- h(x) f(y(x))= 0 \] with either \(y(0)= y(1)= y''(0)= y''(1)= 0\) or \(y(0)= y'(1)= y''(0)= y'''(1)= 0\). We show the existence of at least one positive solution if \(f\) is either superlinear or sublinear by a simple application of a fixed point theorem in cones.
Reviewer: Ma Ruyun (Lanzhou)

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
34C11 Growth and boundedness of solutions to ordinary differential equations
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