×

Existence and uniqueness of monotone positive solutions for an elastic beam equation with nonlinear boundary conditions. (English) Zbl 1247.74035

Summary: We are concerned with the existence and uniqueness of monotone positive solutions for an elastic beam equation with nonlinear boundary conditions. The proof of our main results is based upon a new fixed point theorem of generalized concave operators.

MSC:

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
34B15 Nonlinear boundary value problems for ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Agarwal, R.P., On fourth-order boundary value problems arising in beam analysis, Differential integral equations, 2, 91-110, (1989) · Zbl 0715.34032
[2] Alves, E.; Ma, T.F.; Pelicer, M.L., Monotone positive solutions for a fourth order equation with nonlinear boundary conditions, Nonlinear anal., 71, 3834-3841, (2009) · Zbl 1177.34030
[3] Bai, Z., The upper and lower solution method for some fourth-order boundary value problems, Nonlinear anal., 67, 1704-1709, (2007) · Zbl 1122.34010
[4] Graef, J.R.; Yang, B., Positive solutions of a nonlinear fourth order boundary value problem, Commun. appl. nonl. anal., 14, 1, 61-73, (2007) · Zbl 1136.34024
[5] Li, Y., Two-parameter nonresonance condition for the existence of fourth-order boundary value problems, J. math. anal. appl., 308, 121-128, (2005) · Zbl 1071.34016
[6] Liu, B., Positive solutions of fourth-order two-point boundary value problems, Appl. math. comput., 148, 407-420, (2004) · Zbl 1039.34018
[7] Ma, R.; Wang, H., On the existence of positive solutions of fourth-order ordinary differential equations, Appl. anal., 59, 225-231, (1995) · Zbl 0841.34019
[8] Pei, M.; Chang, S.K., Monotone iterative technique and symmetric positive solutions for a fourth-order boundary value problem, Math. comput. modelling, 51, 1260-1267, (2010) · Zbl 1206.65188
[9] Yang, B., Positive solutions for the beam equation under certain boundary conditions, Electron. J. diff. eqns., 2005, 78, 1-8, (2005) · Zbl 1075.34025
[10] Yao, Q., Positive solutions for eigenvalue problems of fourth-order elastic beam equations, Appl. math. lett., 17, 237-243, (2004) · Zbl 1072.34022
[11] Zhang, X.P., Existence and iteration of monotone positive solutions for an elastic beam with a corner, Nonl. anal. RWA, 10, 2097-2103, (2009) · Zbl 1163.74478
[12] Zhai, C.B.; Yang, C.; Zhang, X.Q., Positive solutions for nonlinear operator equations and several classes of applications, Math. Z., 266, 43-63, (2010) · Zbl 1198.47078
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.