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Positive solutions for \((n-1,1)\) conjugate boundary value problems. (English) Zbl 0871.34015

We are concerned with positive solutions of the nonlinear \((n-1,1)\) conjugate boundary value problem, \[ \begin{aligned} u^{(n)}+ a(t)f(u) &=0, \qquad 0<t<1,\\ u^{(k)}(0) &=0, \qquad 0\leq k\leq n-2,\\ u(1) &= 0,\end{aligned} \] where \(f:[0,\infty)\to [0,\infty)\) is continuous; and \(a:[0,1]\to [0,\infty)\) is continuous and does not vanish identically on any subinterval.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
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