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Davis, John M.; Henderson, Johnny

Triple positive solutions for \((k, n - k)\) conjugate boundary value problems. (English) Zbl 0996.34017

Math. Slovaca 51, No. 3, 313-320 (2001).
Summary: For the \(n\)th-order differential equation \[ (-1)^{n-k} y^{(n)} - f(y) = 0, \quad t\in [0,1], \] satisfying the boundary conditions \(y^{(i)}(0) = 0\), \(0\leq i \leq k-1\), and \(y^{(j)}(1) = 0\), \(0 \leq j \leq n-k-1\), with \(f:\mathbb{R}\to [0, \infty)\), growth conditions are imposed on \(f\) which yield the existence of at least three positive solutions.

Cited in 8 Documents

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations

Keywords:

ordinary differential equation; boundary value problem; Green function; multiple solution; fixed-point
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References:

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