46 citations · 61 across the 8 of their papers we have counts for
8 papers
New definitions of a solution of a one-dimensional elliptic equation with a singular first order divergence term
Daniela Giachetti, Pedro Jesús Martínez-Aparicio, François Murat +1
In this paper, which is a continuation of our recent paper [1], we give two new definitions of a weak solution of the one-dimensional, elliptic, nonlinear singular problem which is…
Multiplicity of solutions for semilinear Robin problems involving sign-changing nonlinearities
José Carmona Tapia, Antonio J. Martínez Aparicio, Pedro J. Martínez-Aparicio
In this article, we investigate the existence and multiplicity of solutions to the Robin problem \begin{equation*} \begin{cases} -Δu = λf(u) & \text{in } Ω, \frac{\partial u}{\part…
Regularizing effect of the natural growth term in quasilinear problems with sign-changing nonlinearities
José Carmona Tapia, Paolo Malanchini, Antonio J. Martínez Aparicio +1
We investigate the existence and nonexistence of solutions to the Dirichlet problem \begin{equation*} \tag{} \label{pba} \left\{ \begin{alignedat}{2} -Δ_p u + g(u) |\nabla u|^p…
Intervals of bifurcation points for semilinear elliptic problems
José Carmona Tapia, Antonio J. Martínez Aparicio, Pedro J. Martínez-Aparicio
In this paper, we study the behavior of multiple continua of solutions to the semilinear elliptic problem \begin{equation*} \begin{cases} -Δu = λf(u) &\text{ in } Ω, u=0 &\text{ on…
Unexpected phenomena in a one dimensional elliptic equation with a singular first order divergence term
Daniela Giachetti, Pedro J. Martínez-Aparicio, François Murat +1
We study existence of a weak solution for one-dimensional problems as \begin{equation}\label{intro}\tag{1} \begin{cases} \displaystyle -\frac{d}{dx}\left(a(x) \frac{d u}{dx}\right)…
Homogenization of a Dirichlet semilinear elliptic problem with a strong singularity at in a domain with many small holes
Daniela Giachetti, Pedro J. Martínez-Aparicio, François Murat
We perform the homogenization of the semilinear elliptic problem \begin{equation*} \begin{cases} u^\varepsilon \geq 0 & \mbox{in} \; Ω^\varepsilon,\\ \displaystyle - div \,A(x) D u…
Definition, existence, stability and uniqueness of the solution to a semilinear elliptic problem with a strong singularity at
Daniela Giachetti, Pedro J. Martínez-Aparicio, François Murat
In this paper we consider a semilinear elliptic equation with a strong singularity at , namely $ \displaystyle u\geq 0 \mbox{ in } Ω$, $ \displaystyle - div \,A(x) D u = F(x,u…
A semilinear elliptic equation with a mild singularity at : existence and homogenization
Daniela Giachetti, Pedro J. Martínez-Aparicio, François Murat
In this paper we consider semilinear elliptic equations with singularities, whose prototype is the following \begin{equation*} \begin{cases} \displaystyle - div \,A(x) D u = f(x)g(…