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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.

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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References:

[1] DOI: 10.1080/00036810008840810 · Zbl 1031.34025
[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
[5] DOI: 10.1016/S0898-1221(01)00188-2 · Zbl 1006.34022
[6] Guo D.J., Functional Methods for Nonlinear Ordinary Differential Equations (1995)
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