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

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.


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