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

Róbert Vrábeľ

Mathematica Bohemica (1997)

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

Abstract

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The paper establishes sufficient conditions for the existence of solutions of Neumann’s problem for the differential equation μ y " + k y = f ( t , y ) which tend to the solution of the reduced problem k y = f ( t , y ) on [ 0 , 1 ] as μ → 0 .

How to cite

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Vrábeľ, 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

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  1. 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
  2. J. Mawhin, Points fixes, points critiques ct problemes aux limites, Sémin. Math. Sup. no. 92, Presses Univ. Montгéal, Montréal, 1985. (1985) MR0789982
  3. K. W. Chang F. A. Howes, Nonlinear singular perturbation phenomena, Springer-Verlag, 1984. (1984) MR0764395

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