# Upper and lower solutions for singularly perturbed semilinear Neumann's problem

Mathematica Bohemica (1997)

- Volume: 122, Issue: 2, page 175-180
- ISSN: 0862-7959

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topVrábeľ, Róbert. "Upper and lower solutions for singularly perturbed semilinear Neumann's problem." Mathematica Bohemica 122.2 (1997): 175-180. <http://eudml.org/doc/248137>.

@article{Vrábeľ1997,

abstract = {The paper establishes sufficient conditions for the existence of solutions of Neumann’s problem for the differential equation $\mu y"+ky=f(t,y)$ which tend to the solution of the reduced problem $ky=f(t,y)$ on $[0,1]$ as $\mu \rightarrow 0.$},

author = {Vrábeľ, Róbert},

journal = {Mathematica Bohemica},

keywords = {singularly perturbed equation; Neumann’s problem; singularly perturbed equation; Neumann's problem},

language = {eng},

number = {2},

pages = {175-180},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Upper and lower solutions for singularly perturbed semilinear Neumann's problem},

url = {http://eudml.org/doc/248137},

volume = {122},

year = {1997},

}

TY - JOUR

AU - Vrábeľ, Róbert

TI - Upper and lower solutions for singularly perturbed semilinear Neumann's problem

JO - Mathematica Bohemica

PY - 1997

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 122

IS - 2

SP - 175

EP - 180

AB - The paper establishes sufficient conditions for the existence of solutions of Neumann’s problem for the differential equation $\mu y"+ky=f(t,y)$ which tend to the solution of the reduced problem $ky=f(t,y)$ on $[0,1]$ as $\mu \rightarrow 0.$

LA - eng

KW - singularly perturbed equation; Neumann’s problem; singularly perturbed equation; Neumann's problem

UR - http://eudml.org/doc/248137

ER -

## References

top- R. E. O'Malley, Jr., 10.1016/0022-247X(76)90214-6, J. Math. Anal. Appl. 54, (1976), 449-466. (1976) Zbl0334.34050MR0450722DOI10.1016/0022-247X(76)90214-6
- J. Mawhin, Points fixes, points critiques ct problemes aux limites, Sémin. Math. Sup. no. 92, Presses Univ. Montгéal, Montréal, 1985. (1985) MR0789982
- K. W. Chang F. A. Howes, Nonlinear singular perturbation phenomena, Springer-Verlag, 1984. (1984) MR0764395

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