5 papers
New definitions of a solution of a one-dimensional elliptic equation with a singular first order divergence term
Daniela Giachetti, Pedro Jesús MartÃnez-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…
Regularizing effect of the natural growth term in quasilinear problems with sign-changing nonlinearities
José Carmona Tapia, Paolo Malanchini, Antonio J. MartÃnez Aparicio +1
We investigate the existence and nonexistence of solutions to the Dirichlet problem \begin{equation*} \tag{} \label{pba} \left\{ \begin{alignedat}{2} -Î_p u + g(u) |\nabla u|^p…
Multiplicity of solutions for semilinear Robin problems involving sign-changing nonlinearities
José Carmona Tapia, Antonio J. MartÃnez Aparicio, Pedro J. MartÃnez-Aparicio
In this article, we investigate the existence and multiplicity of solutions to the Robin problem \begin{equation*} \begin{cases} -Îu = λf(u) & \text{in } Ω, \frac{\partial u}{\p…
Intervals of bifurcation points for semilinear elliptic problems
José Carmona Tapia, Antonio J. MartÃnez Aparicio, Pedro J. MartÃnez-Aparicio
In this paper, we study the behavior of multiple continua of solutions to the semilinear elliptic problem \begin{equation*} \begin{cases} -Îu = λf(u) &\text{ in } Ω, u=0 &\text{…
Unexpected phenomena in a one dimensional elliptic equation with a singular first order divergence term
Daniela Giachetti, Pedro J. MartÃnez-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)…