Existence of nonnegative solutions of singular boundary-value problems for second-order ordinary differential equations
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVIII, Tome 323 (2005), pp. 215-222
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It is proved that the boundary-value problem
$$
-u''+p(t)u+q(t)u^n=f(t), \quad u(a)=u(b)=0, \quad n\ge 2,
$$
has a unique nonnegative solution if the following conditions are fulfilled:
\begin{gather*}
0\le q (t)[(b-t)(t-a)]^{\frac{n+1}{2}}\in L(a,b); \quad 0\le f(t)\sqrt{(b-t)(t-a)}\in L(a,b);
\\
1-\frac1{b-a}\int^{b}_{a}p^-(t)(t-a)(b-t)dt>0.
\end{gather*}
Bibliography: 2 titles.
@article{ZNSL_2005_323_a13,
author = {M. N. Yakovlev},
title = {Existence of nonnegative solutions of singular boundary-value problems for second-order ordinary differential equations},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {215--222},
publisher = {mathdoc},
volume = {323},
year = {2005},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a13/}
}
TY - JOUR AU - M. N. Yakovlev TI - Existence of nonnegative solutions of singular boundary-value problems for second-order ordinary differential equations JO - Zapiski Nauchnykh Seminarov POMI PY - 2005 SP - 215 EP - 222 VL - 323 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a13/ LA - ru ID - ZNSL_2005_323_a13 ER -
%0 Journal Article %A M. N. Yakovlev %T Existence of nonnegative solutions of singular boundary-value problems for second-order ordinary differential equations %J Zapiski Nauchnykh Seminarov POMI %D 2005 %P 215-222 %V 323 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a13/ %G ru %F ZNSL_2005_323_a13
M. N. Yakovlev. Existence of nonnegative solutions of singular boundary-value problems for second-order ordinary differential equations. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVIII, Tome 323 (2005), pp. 215-222. http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a13/