Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {M. N. Yakovlev},
     title = {Existence of nonnegative solutions of singular boundary-value problems for second-order ordinary differential equations},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a13/}
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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/

[1] M. N. Yakovlev, “Razreshimost nelineinykh uravnenii v konuse prostranstva Banakha”, Zap. nauchn. semin. POMI, 248, 1998, 225–230 | MR | Zbl

[2] M. N. Yakovlev, “Razreshimost singulyarnykh kraevykh zadach dlya obyknovennykh differentsialnykh uravnenii poryadka $2m$”, Zap. nauchn. semin. POMI, 309, 2004, 174–188 | MR | Zbl