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Positive solutions of fourth-order boundary value problems with two parameters. (English) Zbl 1030.34016
Summary: Here, the existence of positive solutions are obtained for the fourth-order boundary value problem \[ u^{(4)}+ \beta u''-\alpha u=f(t, u),\;0<t<1,\quad u(0)=u(1)= u''(0)=u''(1)=0, \] where \(f:[0,1] \times\mathbb{R}^+ \to\mathbb{R}^+\) is continuous, \(\alpha,\beta \in\mathbb{R}\) and satisfy \(\beta<2 \pi^2\), \(\alpha\geq- \beta^2/4\), \(\alpha/\pi^4+\beta/ \pi^2<1\).

MSC:
34B08 Parameter dependent boundary value problems for ordinary differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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