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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.

##### MSC:
 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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##### References:
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