arXiv subjects
Publications and source records attributed to Faouzi Haddouchi.
This paper deals with left invertibility problem of implicit hyperbolic systems with delays in infinite dimensional Hilbert spaces. From a decomposition procedure, invertibility for this class of systems is shown to be equivalent to the left invertibility of a subsystem without delays.
We investigate the existence of positive solutions to the nonlinear second-order three-point integral boundary value problem \begin{equation*} \label{eq-1} \begin{gathered} {u^{\prime \prime}}(t)+f(t, u(t))=0,\ 0<t<T, \\ u(0)=βu(η),\ u(T)=α\int_{0}^ηu(s)ds, \end{gathered} \end{equation*} where $0<η<T$, $0<α< \frac{2T}{η^{2}}$, $0<β<\frac{2T-αη^{2}}{αη^{2}-2η+2T}$ are given constants. We establish the existence of at least three positive solutions by using the Leggett-Williams fixed-point theorem.
We investigate the existence of positive solutions to the nonlinear second-order three-point integral boundary value problem \label{eq-1} {u^{\prime \prime}}(t)+a(t)f(u(t))=0,\ 0<t<T, u(0)=βu(η),\ u(T)=α\int_{0}^ηu(s)ds, where $0<η<T$, $0<α< \frac{2T}{η^{2}}$, $0\leqβ<\frac{2T-αη^{2}}{αη^{2}-2η+2T}$ are given constants. We show the existence of at least one positive solution if $f$ is either superlinear or sublinear by applying Krasnoselskii's fixed point theorem in cones.
The proof of a result of J. J. Nieto [3] appeared in "Acta Math, Hung". (1992) concerning the positive solutions of nonlinear problems at resonance is corrected and improved.