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Existence of positive solutions for fourth-order boundary value problem with variable parameters. (English) Zbl 1113.34008

Summary: By using a fixed-point theorem and an operator spectral theorem, the author establishes the existence of positive solutions for the fourth-order boundary value problem: \[ \begin{cases} u^{(4)}+B(t)u''-A(t)u=f(t,u), \quad 0<t<1\\ u(0)=u(1)= u''(0)=u''(1)=0\end{cases} \] where \(A(t)\), \(B(t)\in C[0,1]\) and \(f(t,u):[0,1] \times [0,\infty)\to[0,\infty)\) are continuous.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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