# Positive solutions to nonlinear singular second order boundary value problems

Annales Polonici Mathematici (1996)

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

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topGabriele 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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- [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
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- [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] 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] D. O'Regan, Positive solutions to singular and nonsingular second order boundary value problems, J. Math. Anal. Appl. 142 (1989), 40-52.
- [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] S. D. Taliaferro, A nonlinear singular boundary value problem, Nonlinear Anal. 3 (1979), 897-904. Zbl0421.34021

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