Existence Results for Nonlinear Boundary Value Problems

Abdeljabbar Ghanmi, Samah Horrigue


In the present paper, we are concerned to prove under some hypothesis the existence of fixed points of
the operator $L$ defined on $C(I)$ by
Lu(t)=\int_{0}^{w}G(t,s)h(s)f(u(s))ds,\;t\in I,\,\omega \in \{1,\infty\}
where the functions $f\in C([0,\infty );[0,\infty )),\,h\in C(I;[0,\infty ))$, \\$G\in
C(I\times I)$ and $\begin{cases}
& I=[0,1]\text{ if},\, \omega=1,\\
&I=[0,\infty)\text{ if},\,\omega=\infty.
\end{cases}$. By using Guo Krasnoselskii fixed point theorem, we establish the existence of at least
one fixed point of the operator $L$.

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