# An existence theorem of positive solutions to a singular nonlinear boundary value problem

Commentationes Mathematicae Universitatis Carolinae (1995)

- Volume: 36, Issue: 4, page 609-614
- ISSN: 0010-2628

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topBonanno, Gabriele. "An existence theorem of positive solutions to a singular nonlinear boundary value problem." Commentationes Mathematicae Universitatis Carolinae 36.4 (1995): 609-614. <http://eudml.org/doc/247753>.

@article{Bonanno1995,

abstract = {In this note we consider the boundary value problem $y^\{\prime \prime \}=f(x,y,y^\{\prime \})$$\,(x\in [0,X];X>0)$, $y(0)=0$, $y(X)=a>0$; where $f$ is a real function which may be singular at $y=0$. We prove an existence theorem of positive solutions to the previous problem, under different hypotheses of Theorem 2 of L.E. Bobisud [J. Math. Anal. Appl. 173 (1993), 69–83], that extends and improves Theorem 3.2 of D. O’Regan [J. Differential Equations 84 (1990), 228–251].},

author = {Bonanno, Gabriele},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {ordinary differential equations; singular boundary value problem; positive solutions; positive solution; second order boundary value problem; fixed point theorem for weakly compact, weakly continuous maps},

language = {eng},

number = {4},

pages = {609-614},

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

title = {An existence theorem of positive solutions to a singular nonlinear boundary value problem},

url = {http://eudml.org/doc/247753},

volume = {36},

year = {1995},

}

TY - JOUR

AU - Bonanno, Gabriele

TI - An existence theorem of positive solutions to a singular nonlinear boundary value problem

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1995

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

VL - 36

IS - 4

SP - 609

EP - 614

AB - In this note we consider the boundary value problem $y^{\prime \prime }=f(x,y,y^{\prime })$$\,(x\in [0,X];X>0)$, $y(0)=0$, $y(X)=a>0$; where $f$ is a real function which may be singular at $y=0$. We prove an existence theorem of positive solutions to the previous problem, under different hypotheses of Theorem 2 of L.E. Bobisud [J. Math. Anal. Appl. 173 (1993), 69–83], that extends and improves Theorem 3.2 of D. O’Regan [J. Differential Equations 84 (1990), 228–251].

LA - eng

KW - ordinary differential equations; singular boundary value problem; positive solutions; positive solution; second order boundary value problem; fixed point theorem for weakly compact, weakly continuous maps

UR - http://eudml.org/doc/247753

ER -

## References

top- Arino O., Gautier S., Penot J.P., A fixed point theorem for sequentially continuous mappings with application to ordinary differential equations, Funkcial. Ekv. 27 (1984), 273-279. (1984) Zbl0599.34008MR0794756
- Bobisud L.E., Existence of positive solutions to some nonlinear singular boundary value problems on finite and infinite intervals, J. Math. Anal. Appl. 173 (1993), 69-83. (1993) Zbl0777.34017MR1205910
- Diestel J., Uhl J.J., Vector Measures, Math. Survey, no. 15, Amer. Soc., 1977. Zbl0521.46035MR0453964
- O'Regan D., Existence of positive solutions to some singular and nonsingular second order boundary value problems, J. Differential Equations 84 (1990), 228-251. (1990) Zbl0706.34030MR1047568

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