# Solvability of some singular and nonsingular nonlinear third order boundary value problems

Annales Polonici Mathematici (1991)

- Volume: 54, Issue: 2, page 183-194
- ISSN: 0066-2216

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topD. O'Regan. "Solvability of some singular and nonsingular nonlinear third order boundary value problems." Annales Polonici Mathematici 54.2 (1991): 183-194. <http://eudml.org/doc/262523>.

@article{D1991,

abstract = {Existence of positive solution to certain classes of singular and nonsingular third order nonlinear two point boundary value problems is examined using the idea of Topological Transversality.},

author = {D. O'Regan},

journal = {Annales Polonici Mathematici},

keywords = {Existence of positive solutions; topological transversality theorem; a priori bounds},

language = {eng},

number = {2},

pages = {183-194},

title = {Solvability of some singular and nonsingular nonlinear third order boundary value problems},

url = {http://eudml.org/doc/262523},

volume = {54},

year = {1991},

}

TY - JOUR

AU - D. O'Regan

TI - Solvability of some singular and nonsingular nonlinear third order boundary value problems

JO - Annales Polonici Mathematici

PY - 1991

VL - 54

IS - 2

SP - 183

EP - 194

AB - Existence of positive solution to certain classes of singular and nonsingular third order nonlinear two point boundary value problems is examined using the idea of Topological Transversality.

LA - eng

KW - Existence of positive solutions; topological transversality theorem; a priori bounds

UR - http://eudml.org/doc/262523

ER -

## References

top- [1] R. P. Agarwal, Some new results on two-point problems for higher order differential equations, Funkc. Ekvac. 29 (1986), 197-212. Zbl0623.34019
- [2] R. P. Agarwal, Existence-uniqueness and iterative methods for third-order boundary value problems, J. Comput. Appl. Math. 17 (1987), 271-289. Zbl0617.34008
- [3] L. E. Bobisud and D. O'Regan, Existence of solutions to some singular initial value problems, J. Math. Anal. Appl. 133 (1988), 214-230. Zbl0646.34003
- [4] J. Dugundji and A. Granas, Fixed Point Theory, Vol. 1, Monograf. Mat. 61, PWN, Warszawa 1982.
- [5] A. Granas, R. B. Guenther and J. W. Lee, Nonlinear boundary value problems for ordinary differential equations, Dissertationes Math. 244 (1985). Zbl0615.34010
- [6] A. Granas, R. B. Guenther and J. W. Lee, Nonlinear boundary value problems for some classes of ordinary differential equations, Rocky Mountain J. Math. 10 (1980), 35-58. Zbl0476.34017
- [7] L. K. Jackson, Existence and uniqueness of solutions of boundary value problems for Lipschitz equations, J. Differential Equations 32 (1979), 76-90. Zbl0407.34018
- [8] D. O'Regan, Topological transversality: Applications to third order boundary value problems, SIAM J. Math. Anal. 18 (3) (1987), 630-641. Zbl0628.34017
- [9] D. O'Regan, Singular and nonsingular third order boundary value problems, Proc. Royal Irish Acad. 90A (1990), 29-42.
- [10] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York 1966.
- [11] S. D. Taliaferro, A nonlinear singular boundary value problem, Nonlinear Anal. 3 (1979), 897-904. Zbl0421.34021

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