caa a22 4500 475741846 CHVBK 20180406123501.0 cr unu---uuuuu 170329e20000401xx s 000 0 eng 10.1007/BF02676400 doi (NATIONALLICENCE)springer-10.1007/BF02676400 Existence of solutions with turning points for nonlinear singularly perturbed boundary-value problems [Elektronische Daten] [A. Kolesov, N. Rozov] We consider the following singularly perturbed boundary-value problem: $$\varepsilon u'' = f\left( {x,u,u'} \right), 0< \varepsilon \ll 1, g_j \left( {u\left| {_{x = 0} ,} \right.u\left| {_{x = 1} ,u'\left| {_{x = 0} ,} \right.} \right.u'\left| {_{x = 1} } \right.} \right) = 0, j = 1,2,$$ on the interval 0 ≤x ≤ 1. We study the existence and uniqueness of its solutionu(x, ε) having the following properties:u(x, ε) →u 0(x) asε → 0 uniformly inx ε [0, 1], whereu 0(x) εC ∞ [0, 1] is a solution of the degenerate equationf(x, u, u′)=0; there exists a pointx 0 ε (0, 1) such thata(x 0)=0,a′(x 0) > 0,a(x) < 0 for 0 ≤x <x 0, anda(x) > 0 forx 0 <x ≤ 1, wherea(x)=f′ v(x,u 0(x),u′ 0(x)). Kluwer Academic/Plenum Publishers, 2000 nonlinear boundary-value problem nationallicence singular perturbation nationallicence solution with turning points nationallicence existence and uniqueness of solutions nationallicence Kolesov A. P. G. Demidov Yaroslavl State University, USSR aut Rozov N. M. V. Lomonosov Moscow State University, USSR aut Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/4(2000-04-01), 444-447 0001-4346 67:4<444 2000 67 11006 https://doi.org/10.1007/BF02676400 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02676400 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kolesov A. P. G. Demidov Yaroslavl State University, USSR aut NATIONALLICENCE 700 1- Rozov N. M. V. Lomonosov Moscow State University, USSR aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/4(2000-04-01), 444-447 0001-4346 67:4<444 2000 67 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer