# Sufficient conditions for the solvability of some third order functional boundary value problems on the half-line

Commentationes Mathematicae Universitatis Carolinae (2017)

- Volume: 58, Issue: 4, page 443-459
- ISSN: 0010-2628

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topCarrasco, Hugo, and Minhós, Feliz. "Sufficient conditions for the solvability of some third order functional boundary value problems on the half-line." Commentationes Mathematicae Universitatis Carolinae 58.4 (2017): 443-459. <http://eudml.org/doc/294769>.

@article{Carrasco2017,

abstract = {This paper is concerned with the existence of bounded or unbounded solutions to third-order boundary value problem on the half-line with functional boundary conditions. The arguments are based on the Green functions, a Nagumo condition, Schauder fixed point theorem and lower and upper solutions method. An application to a Falkner-Skan equation with functional boundary conditions is given to illustrate our results.},

author = {Carrasco, Hugo, Minhós, Feliz},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {functional boundary conditions; unbounded solutions; half-line; upper and lower solutions; Nagumo condition; Green's function; fixed point theory; Falkner-Skan equation},

language = {eng},

number = {4},

pages = {443-459},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Sufficient conditions for the solvability of some third order functional boundary value problems on the half-line},

url = {http://eudml.org/doc/294769},

volume = {58},

year = {2017},

}

TY - JOUR

AU - Carrasco, Hugo

AU - Minhós, Feliz

TI - Sufficient conditions for the solvability of some third order functional boundary value problems on the half-line

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2017

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 58

IS - 4

SP - 443

EP - 459

AB - This paper is concerned with the existence of bounded or unbounded solutions to third-order boundary value problem on the half-line with functional boundary conditions. The arguments are based on the Green functions, a Nagumo condition, Schauder fixed point theorem and lower and upper solutions method. An application to a Falkner-Skan equation with functional boundary conditions is given to illustrate our results.

LA - eng

KW - functional boundary conditions; unbounded solutions; half-line; upper and lower solutions; Nagumo condition; Green's function; fixed point theory; Falkner-Skan equation

UR - http://eudml.org/doc/294769

ER -

## References

top- Agarwal R.P., O'Regan D., Infinite Interval Problems for Differential, Difference and Integral Equations, Kluwer Academic Publisher, Glasgow, 2001. Zbl0988.34002MR1845855
- Boucherif A., 10.1016/j.na.2007.12.007, Nonlinear Anal. 70 (2009) no. 1, 364–371. Zbl1169.34310MR2468243DOI10.1016/j.na.2007.12.007
- Cabada A., Fialho J., Minhós F., Non ordered lower and upper solutions to fourth order functional BVP, Discrete Contin. Dyn. Syst. 2011, Suppl. Vol. I, 209–218. MR2987401
- Cabada A., Minhós F., 10.1016/j.jmaa.2007.08.026, J. Math. Anal. Appl. 340 (2008), 239–251. Zbl1138.34008MR2376151DOI10.1016/j.jmaa.2007.08.026
- Corduneanu C., Integral Equations and Applications, Cambridge University Press, Cambridge, 1991. Zbl1156.45001MR1109491
- Feng H., Ji D., Ge W., 10.1016/j.na.2008.07.013, Nonlinear Anal. 70 (2009), 3761–3566. MR2502764DOI10.1016/j.na.2008.07.013
- Fialho J., Minhós F., Higher order functional boundary value problems without monotone assumptions, Bound. Value Probl. 2013, 2013:81. Zbl1293.34027MR3055842
- Fu D., Ding W., Existence of positive solutions of third-order boundary value problems with integral boundary conditions in Banach spaces, Adv. Difference Equ. 2013, 2013:65. MR3044690
- Graef J., Kong L., Minhós F., Fialho J., 10.2298/AADM110221010G, Appl. Anal. Discrete Math. 5 (2011), no. 1, 133–146. Zbl1289.34054MR2809041DOI10.2298/AADM110221010G
- Graef J., Kong L., Minhós F., 10.1007/s12591-010-0071-1, Differ. Equ. Dyn. Syst. 18 (2010), no. 4, 373–383. MR2775180DOI10.1007/s12591-010-0071-1
- Han J., Liu Y., Zhao J., Integral boundary value problems for first order nonlinear impulsive functional integro-differential differential equations, Appl. Math. Comput. 218 (2012), 5002–5009. MR2870024
- Jiang J., Liu L., Wu Y., Second-order nonlinear singular Sturm Liouville problems with integral boundary conditions, Appl. Math. Comput. 215 (2009), 1573–1582. MR2571646
- Kong L., Wong J., 10.1016/j.jmaa.2010.01.063, J. Math. Anal. Appl. 367 (2010), 588–611. Zbl1197.34035MR2607284DOI10.1016/j.jmaa.2010.01.063
- Lu H., Sun L., Sun J., Existence of positive solutions to a non-positive elastic beam equation with both ends fixed, Bound. Value Probl. 2012, 2012:56. MR2942969
- Minhós F., Fialho J., On the solvability of some fourth-order equations with functional boundary conditions, Discrete Contin. Dyn. Syst., 2009, suppl., 564–573. Zbl1192.34023MR2648180
- Pei M., Chang S., Oh Y.S., Solvability of right focal boundary value problems with superlinear growth conditions, Bound. Value Probl. 2012, 2012:60. MR2965952
- Yoruk F., Aykut Hamal N., Second-order boundary value problems with integral boundary conditions on the real line, Electronic J. Differential Equations, vol. 2014 (2014), no. 19, 1–13. Zbl1292.34017MR3159428
- Wang M.X., Cabada A., Nieto J.J., 10.4064/ap-58-3-221-235, Ann. Polon. Math. 58 (1993), 221–235. Zbl0789.34027MR1244394DOI10.4064/ap-58-3-221-235
- Zeidler E., Nonlinear Functional Analysis and Its Applications, I: Fixed-Point Theorems, Springer, New York, 1986. Zbl0583.47050MR0816732
- Zhang Z., Zhang C., Similarity solutions of a boundary layer problem with a negative parameter arising in steady two-dimensional flow for power-law fluids, Nonlinear Anal. 102 (2014), 1–13. Zbl1292.76005MR3182794
- Zhu S., Wu Q., Cheng X., Numerical solution of the Falkner-Skan equation based on quasilinearization, Appl. Math. Comput. 215 (2009), 2472–2485. MR2563461

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