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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.

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
Full Text: DOI
[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)
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