zbMATH — the first resource for mathematics

Existence and nonexistence for a singular boundary value problem. (English) Zbl 0628.34025
Existence of positive solutions of the two-point boundary value problem \(y''=\lambda ^ 2f(x,y)\), \(y(0)=a>0\), \(y(1)=b\geq 0\) is studied, where \(\lambda ^ 2>0\) and \(\int _{0}f(x,y)dy<\infty\) but \(\lim _{y\to 0}f(x,y)=\infty.\) It is shown that positive solutions exist provided \(\lambda ^ 2\) is sufficiently small but that no positive solutions exist for \(\lambda ^ 2\) large.

34B15 Nonlinear boundary value problems for ordinary differential equations
34C11 Growth and boundedness of solutions to ordinary differential equations
Full Text: DOI
[1] Aris R., Mathematical Theory of Diffusion and Reaction in Permeable Catalysts (1975) · Zbl 0315.76051
[2] Bobisud L. E., J. Math. Anal. Appl (1975)
[3] DOI: 10.1080/00036818608839643 · Zbl 0584.34012 · doi:10.1080/00036818608839643
[4] DOI: 10.1016/0022-0396(70)90106-3 · Zbl 0201.43102 · doi:10.1016/0022-0396(70)90106-3
[5] Granas A., Dissertationes Mathe-matcae 7 (1985)
[6] DOI: 10.1137/0512073 · Zbl 0478.34021 · doi:10.1137/0512073
[7] DOI: 10.1016/0362-546X(78)90050-0 · Zbl 0383.34003 · doi:10.1016/0362-546X(78)90050-0
[8] DOI: 10.1016/0362-546X(79)90057-9 · Zbl 0421.34021 · doi:10.1016/0362-546X(79)90057-9
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.