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Singular Sturm-Liouville problems and existence of solutions to singular nonlinear boundary value problems. (English) Zbl 0780.34017
From the introduction: “This paper establishes existence results for second order boundary value problems of the form \(p^{-1}(t) (p(t) y'(t))'= q(t)(f(t,y(t),p(t) y'(t))\), \(0<t<1\), \(y(1)=\lim_{t\to+0} p(t) y'(t)=0\), where \(f: [0,1]\times \mathbb{R}^ 2\to\mathbb{R}\) is continuous, \(q\in C(0,1)\), \(p\in C[0,1]\cap C^ 1(0,1]\) with \(p>0\) on \((0,1]\), \(p(0)=0\) and \(\int^ 1_ 0 p^{-1}(s)ds=\infty\)”.

34B24 Sturm-Liouville theory
34B15 Nonlinear boundary value problems for ordinary differential equations
Full Text: DOI
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