×

zbMATH — the first resource for mathematics

Double positive solutions of fourth-order nonlinear boundary value problems. (English) Zbl 1037.34017
The authors consider nonlinear fourth-order differential equations \( u^{(4)}(t)=a(t)f(u(t)),\) \(t\in (0,1)\), subject to several boundary conditions. Under suitable growth conditions on the nonlinearity f and using a generalized Leggett-Williams fixed-point theorem, they show that the given problem has at least two positive solutions.

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: DOI
References:
[1] DOI: 10.1080/00036810008840810 · Zbl 1031.34025 · doi:10.1080/00036810008840810
[2] Krasnosel’skii M.A., Positive Solutions of Operator Equations (1964)
[3] Ma R.Y., J. Math. Anal. Appl 59 pp 225– (1995)
[4] DOI: 10.1006/jmaa.1997.5639 · Zbl 0892.34009 · doi:10.1006/jmaa.1997.5639
[5] DOI: 10.1016/S0898-1221(01)00188-2 · Zbl 1006.34022 · doi:10.1016/S0898-1221(01)00188-2
[6] Guo D.J., Functional Methods for Nonlinear Ordinary Differential Equations (1995)
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.