arXiv subjects
Publications and source records attributed to Slimane Benaicha.
In this paper, we study the existence and multiplicity of positive solutions for a nonlinear fourth-order with multi-point boundary conditions involving an integral boundary condition. The main tool is Krasnosel'skii fixed point theorem on cones.
In this paper, we study the existence of at least one positive solution for a nonlinear third-order two-point boundary value problem with integral condition. By employing the Krasnoselskii's fixed point theorem on cones, the existence results of the problem are established.
This paper is devoted to study the existence of solutions and the monotone method of second-order periodic boundary value problems when the lower and upper solutions $α$ and $β$ violate the boundary conditions $ α(0)=α(2π)$ and $β(0)=β(2π)$. We present several comparison results. We show that the method of lower and upper solutions coupled with the monotone iterative technique is valid to obtain constuctive proof of existence of solutions.
In this paper, the existence of positive solutions for a nonlinear fourth-order two-point boundary value problem with integral condition is investigated. By using Krasnoselskii's fixed point theorem on cones, sufficient conditions for the existence of at least one positive solutions are obtained.
In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP) for the following second-order differential equation \begin{equation*} \begin{gathered} {u^{\prime \prime }}(t)+λa(t)f(u(t))=0,\ \ 0 0$ is a parameter, $0<η<1$, $0<α< \frac{1}{η}$. By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.
In this paper, by using the Krasnosel'skii's fixed-point theorem, we study the existence of at least one or two positive solutions to the three-point integral boundary value problem {equation*} \label{eq-1} {gathered} {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, {gathered} {equation*} where $0<η<T$, $0<α< \frac{2T}{η^{2}}$, $0\leqβ<\frac{2T-αη^{2}}{αη^{2}-2η+2T}$ are given constants.
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.