# Positive solutions to nonlinear singular second order boundary value problems

• Volume: 64, Issue: 3, page 237-251
• ISSN: 0066-2216

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## Abstract

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Existence theorems of positive solutions to a class of singular second order boundary value problems of the form y'' + f(x,y,y') = 0, 0 < x < 1, are established. It is not required that the function (x,y,z) → f(x,y,z) be nonincreasing in y and/or z, as is generally assumed. However, when (x,y,z) → f(x,y,z) is nonincreasing in y and z, some of O'Regan's results [J. Differential Equations 84 (1990), 228-251] are improved. The proofs of the main theorems are based on a fixed point theorem for weakly sequentially continuous operators.

## How to cite

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Gabriele Bonanno. "Positive solutions to nonlinear singular second order boundary value problems." Annales Polonici Mathematici 64.3 (1996): 237-251. <http://eudml.org/doc/269995>.

@article{GabrieleBonanno1996,
abstract = {Existence theorems of positive solutions to a class of singular second order boundary value problems of the form y'' + f(x,y,y') = 0, 0 < x < 1, are established. It is not required that the function (x,y,z) → f(x,y,z) be nonincreasing in y and/or z, as is generally assumed. However, when (x,y,z) → f(x,y,z) is nonincreasing in y and z, some of O'Regan's results [J. Differential Equations 84 (1990), 228-251] are improved. The proofs of the main theorems are based on a fixed point theorem for weakly sequentially continuous operators.},
author = {Gabriele Bonanno},
journal = {Annales Polonici Mathematici},
keywords = {singular boundary value problem; positive solution; positive solutions; singular second order; boundary values problems; weakly sequentially continuous operators},
language = {eng},
number = {3},
pages = {237-251},
title = {Positive solutions to nonlinear singular second order boundary value problems},
url = {http://eudml.org/doc/269995},
volume = {64},
year = {1996},
}

TY - JOUR
AU - Gabriele Bonanno
TI - Positive solutions to nonlinear singular second order boundary value problems
JO - Annales Polonici Mathematici
PY - 1996
VL - 64
IS - 3
SP - 237
EP - 251
AB - Existence theorems of positive solutions to a class of singular second order boundary value problems of the form y'' + f(x,y,y') = 0, 0 < x < 1, are established. It is not required that the function (x,y,z) → f(x,y,z) be nonincreasing in y and/or z, as is generally assumed. However, when (x,y,z) → f(x,y,z) is nonincreasing in y and z, some of O'Regan's results [J. Differential Equations 84 (1990), 228-251] are improved. The proofs of the main theorems are based on a fixed point theorem for weakly sequentially continuous operators.
LA - eng
KW - singular boundary value problem; positive solution; positive solutions; singular second order; boundary values problems; weakly sequentially continuous operators
UR - http://eudml.org/doc/269995
ER -

## References

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1. [1] O. Arino, S. Gautier and J. P. Penot, A fixed point theorem for sequentially continuous mappings with application to ordinary differential equations, Funkcial. Ekvac. 27 (1984), 273-279. Zbl0599.34008
2. [2] L. E. Bobisud, Existence of positive solutions to some nonlinear singular boundary value problems on finite and infinite intervals, J. Math. Anal. Appl. 173 (1993), 69-83. Zbl0777.34017
3. [3] L. E. Bobisud, D. O'Regan and W. D. Royalty, Solvability of some nonlinear boundary value problems, Nonlinear Anal. 12 (1988), 855-869. Zbl0653.34015
4. [4] G. Bonanno, An existence theorem of positive solutions to a singular nonlinear boundary value problem, Comment. Math. Univ. Carolin. 36 (1995), 609-614. Zbl0847.34020
5. [5] A. Callegari and A. Nachman, Some singular, nonlinear differential equations arising in boundary layer theory, J. Math. Anal. Appl. 64 (1978), 96-105. Zbl0386.34026
6. [6] J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., 1977.
7. [7] J. A. Gatica, V. Oliker and P. Waltman, Singular nonlinear boundary value problems for second-order ordinary differential equations, J. Differential Equations 79 (1989), 62-78. Zbl0685.34017
8. [8] A. Nachman and A. Callegari, A nonlinear singular boundary value problem in theory of pseudoplastic fluids, SIAM J. Appl. Math. 38 (1980), 275-281.
9. [9] D. O'Regan, Positive solutions to singular and nonsingular second order boundary value problems, J. Math. Anal. Appl. 142 (1989), 40-52.
10. [10] D. O'Regan, Existence of positive solutions to some singular and nonsingular second order boundary value problems, J. Differential Equations 84 (1990), 228-251.
11. [11] S. D. Taliaferro, A nonlinear singular boundary value problem, Nonlinear Anal. 3 (1979), 897-904. Zbl0421.34021

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