Complete description of the set of solutions to a strongly nonlinear O.D.E's

A. Benmezai, U.S.T.H.B., El-Alia Babezouar Alger, Algérie

E. J. Qualitative Theory of Diff. Equ., No. 9. (2003), pp. 1-18.

Abstract: We give a complete description of the set of solutions to the boundary value problem
\[
\left\{
\begin{array}{c}
-\left( \varphi \left( u^{\prime }\right) \right) ^{\prime }=f\left(
u\right) \text{ in }\left( 0,1\right) \\
u\left( 0\right) =u\left( 1\right) =0
\end{array}
\right.
\]
where $\varphi $ is an odd increasing homeomorphism of $\Bbb{R}$ concave on $\Bbb{R}^{+}$ and $f$ $\in C\left( \Bbb{R}\text{, }\Bbb{R}\right) $is odd and superlinear.

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