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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
##### Keywords:
existence of solutions; boundary value problem
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