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Title: Boundary value problem with an inner point for the singularly perturbed semilinear differential equations (English)
Author: Vrábeľ, Róbert
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 136
Issue: 1
Year: 2011
Pages: 1-8
Summary lang: English
Category: math
Summary: In this paper we investigate the problem of existence and asymptotic behavior of solutions for the nonlinear boundary value problem $$ \epsilon y''+ky=f(t,y),\quad t\in \langle a,b \rangle , \ k<0,\ 0<\epsilon \ll 1 $$ satisfying three point boundary conditions. Our analysis relies on the method of lower and upper solutions and delicate estimations. (English)
Keyword: singular perturbation
Keyword: boundary value problem
Keyword: upper solution
Keyword: lower solution
MSC: 34B10
MSC: 34B16
MSC: 34E05
MSC: 34E10
MSC: 34E20
idZBL: Zbl 1224.34037
idMR: MR2807703
DOI: 10.21136/MB.2011.141442
Date available: 2011-03-31T11:19:12Z
Last updated: 2020-07-29
Stable URL:
Reference: [1] Coster, C. De, Habets, P.: Two-Point Boundary Value Problems: Lower and Upper Solutions.Volume 205 (Mathematics in Science and Engineering), Elsevier (2006). MR 2225284
Reference: [2] Mawhin, J.: Points fixes, points critiques et problemes aux limites.Semin. Math. Sup. no. 92, Presses Univ. Montreal (1985). Zbl 0561.34001, MR 0789982
Reference: [3] Šeda, V.: On some non-linear boundary value problems for ordinary differential equations.Arch. Math., Brno {\it 25} (1989), 207-222. MR 1188065
Reference: [4] Vrábeľ, R.: Asymptotic behavior of T-periodic solutions of singularly perturbed second-order differential equation.Math. Bohem. 121 (1996), 73-76. MR 1388177
Reference: [5] Vrábeľ, R.: Semilinear singular perturbation.Nonlin. Anal. Theory Methods Appl. 25 (1995), 17-26. MR 1331985, 10.1016/0362-546X(94)00123-Y


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