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Some general existence principles and results for \((\varphi(y'))=qf(t,y,y'),0<t<1\). (English) Zbl 0778.34013
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.

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
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