Third order differential equations with integral boundary conditions. (English) Zbl 1238.34031

Summary: We study nonlinear third order differential equations with integral boundary conditions. We provide sufficient conditions on the nonlinearity and the functions appearing in the boundary conditions that guarantee the existence of at least one solution to our problem. Our technique is based on a priori bounds and fixed point theorems.


34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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[1] Aftabizadeh, A.; Gupta, C. P.; Xu, J., Existence and uniqueness theorems for three-point boundary value problems, SIAM J. Math. Anal., 20, 3, 716-726 (1989) · Zbl 0704.34019
[2] Aftabizadeh, A.; Deimling, K., A three-point nonlinear boundary value problem, Differ. Integral Equ., 4, 1, 189-194 (1991) · Zbl 0723.34016
[3] Bernis, F.; Peletier, L. A., Two problems from draining flows involving third-order ordinary differential equations, SIAM J. Math. Anal., 27, 515-527 (1996) · Zbl 0845.34033
[4] Mehri, B.; Niksirat, M. A., On the existence of periodic solutions for certain differential equations, J. Comput. Appl. Math., 174, 239-249 (2005) · Zbl 1069.34064
[5] Boucherif, A.; Al-Malki, N., Nonlinear three-point third order boundary value problems, Appl. Math. Comput., 190, 1168-1177 (2007) · Zbl 1134.34007
[6] Minhós, F. M., On some third order nonlinear boundary value problems: Existence, location and multiplicity results, J. Math. Anal. Appl., 339, 1342-1353 (2008) · Zbl 1144.34009
[7] Belarbi, A.; Benchohra, M., Existence results for nonlinear boundary value problems with integral boundary conditions, Electron. J. Differential Equations, 06, 10 (2005) · Zbl 1075.34015
[8] Brykalov, S. A., A second order nonlinear problem with two-point and integral boundary conditions, Proc. Georgian Acad. Sci. Math., 1, 273-279 (1993) · Zbl 0798.34021
[9] Benbouziane, Z. N.; Boucherif, A.; Bouguima, S. M., Third order nonlocal multipoint boundary value problems, Dynam. Systems Appl., 13, 41-48 (2004) · Zbl 1070.34027
[10] Gray, M., Uniqueness implies uniqueness for nonlocal boundary value problems for third order ordinary differential equations, Dynam. Systems Appl., 16, 277-284 (2007) · Zbl 1153.34008
[11] Wang, Y.; Ge, W., Existence of solutions for a third order differential equation with integral boundary conditions, Comput. Math. Appl., 53, 144-154 (2007) · Zbl 1134.34009
[12] O’Regan, D., Fixed point theory for the sum of two operators, Appl. Math. Lett., 9, 1-8 (1996) · Zbl 0858.34049
[13] Boucherif, A., Second order boundary value problems with integral boundary conditions, Nonlinear Anal., 70, 364-371 (2009) · Zbl 1169.34310
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