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

D. O'Regan

Annales Polonici Mathematici (1991)

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

Abstract

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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.

How to cite

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D. 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

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  1. [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. [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. [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. [4] J. Dugundji and A. Granas, Fixed Point Theory, Vol. 1, Monograf. Mat. 61, PWN, Warszawa 1982. 
  5. [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. [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. [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. [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. [9] D. O'Regan, Singular and nonsingular third order boundary value problems, Proc. Royal Irish Acad. 90A (1990), 29-42. 
  10. [10] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York 1966. 
  11. [11] S. D. Taliaferro, A nonlinear singular boundary value problem, Nonlinear Anal. 3 (1979), 897-904. Zbl0421.34021

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