Previous |  Up |  Next

Article

Keywords:
singular perturbation; boundary value problem; upper solution; lower solution
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.
References:
[1] Coster, C. De, Habets, P.: Two-Point Boundary Value Problems: Lower and Upper Solutions. Volume 205 (Mathematics in Science and Engineering), Elsevier (2006).
[2] Mawhin, J.: Points fixes, points critiques et problemes aux limites. Semin. Math. Sup. no. 92, Presses Univ. Montreal (1985). MR 0789982 | Zbl 0561.34001
[3] Šeda, V.: On some non-linear boundary value problems for ordinary differential equations. Arch. Math., Brno {\it 25} (1989), 207-222. MR 1188065
[4] Vrábeľ, R.: Asymptotic behavior of T-periodic solutions of singularly perturbed second-order differential equation. Math. Bohem. 121 (1996), 73-76. MR 1388177
[5] Vrábeľ, R.: Semilinear singular perturbation. Nonlin. Anal. Theory Methods Appl. 25 (1995), 17-26. DOI 10.1016/0362-546X(94)00123-Y | MR 1331985
Partner of
EuDML logo