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Triple positive solutions for a class of two-point boundary-value problems. (English) Zbl 1055.34046
The existence of at least three positive solutions is proved for the equation $-x'' = q(t) f(t,x,x'),$ subject to the boundary conditions $$x(0)=x(1) = 0$$, or $$x(0)=x'(1) = 0$$, assuming on $$f$$ suitable growth conditions related to the classical super-sublinearity conditions. The result is obtained by applying a fixed-point theorem of R. I. Avery and A. C. Peterson [Comput. Math. Appl. 42, No. 3–5, 313–322 (2001; Zbl 1005.47051)].
##### MSC:
 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations
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