×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: EMIS EuDML