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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References:

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