4 papers
Existence and comparison results for a doubly singular 1-Laplacian problem with data
Antonio J. Martínez Aparicio
In this work, we conduct a comprehensive study of problem \begin{equation*} \begin{cases} -Δ_1 u + g(u)|Du| = h(u)f & \text{in }Ω, u=0 & \text{on } \partialΩ, \end{cases} \end{equa…
Existence and nonexistence of infinitely many solutions to elliptic problems with oscillating nonlinearities
Antonio J. Martínez Aparicio, Clara Torres-Latorre
We study sharp conditions for the existence and nonexistence of infinitely many nonnegative solutions to the problem in a bounded domain with Dirichlet boundary co…
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…
Optimal global regularity for 1-Laplace type BVP's with singular lower order terms
Antonio J. Martínez Aparicio, Francescantonio Oliva, Francesco Petitta
In this paper we provide a complete characterization of the regularity properties of the solutions associated to the homogeneous Dirichlet problem \begin{equation*} \begin{cases} \…