Boundary value problem with an inner point for the singularly perturbed semilinear differential equations

Róbert Vrábeľ

Mathematica Bohemica (2011)

  • Volume: 136, Issue: 1, page 1-8
  • ISSN: 0862-7959

Abstract

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In this paper we investigate the problem of existence and asymptotic behavior of solutions for the nonlinear boundary value problem ϵ y ' ' + k y = f ( t , y ) , t ∈ 〈 a , b 〉 , k < 0 , 0 < ϵ ≪ 1 satisfying three point boundary conditions. Our analysis relies on the method of lower and upper solutions and delicate estimations.

How to cite

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Vrábeľ, Róbert. "Boundary value problem with an inner point for the singularly perturbed semilinear differential equations." Mathematica Bohemica 136.1 (2011): 1-8. <http://eudml.org/doc/196390>.

@article{Vrábeľ2011,
abstract = {In this paper we investigate the problem of existence and asymptotic behavior of solutions for the nonlinear boundary value problem \[ \epsilon y^\{\prime \prime \}+ky=f(t,y),\quad t\in \langle a,b \rangle , \ k<0,\ 0<\epsilon \ll 1 \] satisfying three point boundary conditions. Our analysis relies on the method of lower and upper solutions and delicate estimations.},
author = {Vrábeľ, Róbert},
journal = {Mathematica Bohemica},
keywords = {singular perturbation; boundary value problem; upper solution; lower solution; singular perturbation; boundary value problem; upper solution; lower solution},
language = {eng},
number = {1},
pages = {1-8},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Boundary value problem with an inner point for the singularly perturbed semilinear differential equations},
url = {http://eudml.org/doc/196390},
volume = {136},
year = {2011},
}

TY - JOUR
AU - Vrábeľ, Róbert
TI - Boundary value problem with an inner point for the singularly perturbed semilinear differential equations
JO - Mathematica Bohemica
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 136
IS - 1
SP - 1
EP - 8
AB - In this paper we investigate the problem of existence and asymptotic behavior of solutions for the nonlinear boundary value problem \[ \epsilon y^{\prime \prime }+ky=f(t,y),\quad t\in \langle a,b \rangle , \ k<0,\ 0<\epsilon \ll 1 \] satisfying three point boundary conditions. Our analysis relies on the method of lower and upper solutions and delicate estimations.
LA - eng
KW - singular perturbation; boundary value problem; upper solution; lower solution; singular perturbation; boundary value problem; upper solution; lower solution
UR - http://eudml.org/doc/196390
ER -

References

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  1. Coster, C. De, Habets, P., Two-Point Boundary Value Problems: Lower and Upper Solutions, Volume 205 (Mathematics in Science and Engineering), Elsevier (2006). (2006) MR2225284
  2. Mawhin, J., Points fixes, points critiques et problemes aux limites, Semin. Math. Sup. no. 92, Presses Univ. Montreal (1985). (1985) Zbl0561.34001MR0789982
  3. Šeda, V., On some non-linear boundary value problems for ordinary differential equations, Arch. Math., Brno (1989), 207-222. MR1188065
  4. Vrábeľ, R., Asymptotic behavior of T-periodic solutions of singularly perturbed second-order differential equation, Math. Bohem. 121 (1996), 73-76. (1996) MR1388177
  5. Vrábeľ, R., 10.1016/0362-546X(94)00123-Y, Nonlin. Anal. Theory Methods Appl. 25 (1995), 17-26. (1995) MR1331985DOI10.1016/0362-546X(94)00123-Y

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