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Existence of $n$ solutions and/or positive solutions to a semipositone elastic beam equation. (English) Zbl 1113.34013
This paper considers nonlinear fourth order boundary value problems of the form $$u^{(4)}(t)=f(t,u(t),u''(t)),$$ $$u(0)=u(1)=u''(0)=u''(1)=0.$$ Under certain conditions on the nonlinearity $f$, it is proven that the problem has at least $n$ solutions, where $n$ is any positive integer, under additional conditions these solutions are positive. The proofs of these results are based on the Krasnosel’skii fixed point theorem for compact mappings in subsets of cones.

##### MSC:
 34B15 Nonlinear boundary value problems for ODE 34B18 Positive solutions of nonlinear boundary value problems for ODE
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##### References:
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