O’Regan, Donal Some general existence principles and results for \((\varphi(y'))=qf(t,y,y'),0<t<1\). (English) Zbl 0778.34013 SIAM J. Math. Anal. 24, No. 3, 648-668 (1993). The author discusses the existence of solutions to the boundary value problem \((\varphi(y'))'=q(t)\) \(f(t,y,y')\), \(0<t<1\), \(y(0)=a\), \(y(1)=b\) (or \(y'(0)=a\), \(y(1)=b)\), where \(q\in C(0,1)\), \(f:[0,1]\times\mathbb{R}^ 2\to\mathbb{R}\) and \(\varphi:\mathbb{R}\to\mathbb{R}\) are continuous functions satisfying physically reasonable conditions. In particular, the special case when \(\varphi(v)=v| v|^{n-2}\), \(n>1\), is included. Reviewer: S.Aizicovici (Athens / Ohio) Cited in 1 ReviewCited in 84 Documents MSC: 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:existence of solutions; boundary value problem PDFBibTeX XMLCite \textit{D. O'Regan}, SIAM J. Math. Anal. 24, No. 3, 648--668 (1993; Zbl 0778.34013) Full Text: DOI