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Zbl 0841.34019
Ma, Ruyun; Wang, Haiyan
On the existence of positive solutions of fourth-order ordinary differential equations.
(English)
[J] Appl. Anal. 59, No.1-4, 225-231 (1995). ISSN 0003-6811; ISSN 1563-504X/e

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.
[Ma Ruyun (Lanzhou)]
MSC 2000:
*34B15 Nonlinear boundary value problems of ODE
34C11 Qualitative theory of solutions of ODE: Growth, etc.

Keywords: fourth-order ordinary differential equation; existence of positive solutions

Cited in: Zbl 0989.34066 Zbl 0979.34012

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