5 papers · 1 filter
Touchdown solutions in general MEMS models
Rodrigo Clemente, João Marcos do Ó, Esteban da Silva +1
We study general equations modeling electrostatic MEMS devices \begin{equation} \begin{cases} \label{P} φ\big(r,- u'(r)\big)=λ\int_0^r\frac{f(s)}{g(u(s))}\,\mathrm{d}s, & r\in(0,1)…
Existence of solutions for a fractional Choquard--type equation in with critical exponential growth
Rodrigo Clemente, José Carlos de Albuquerque, Eudes Barboza
In this paper we study the following class of fractional Choquard--type equations \[ (-Δ)^{1/2}u + u=\Big( I_μ\ast F(u)\Big)f(u), \quad x\in\mathbb{R}, \] where denote…
Some elliptic problems with singular nonlinearity and advection for Riemannian manifolds
João Marcos do Ó, Rodrigo Clemente
We are interested in regularity properties of semi-stable solutions for a class of singular semilinear elliptic problems with advection term defined on a smooth bounded domain of a…
On Lane-Emden systems with singular nonlinearities and applications to MEMS
João Marcos do Ó, Rodrigo Clemente
In this paper we analyse the Lane-Emden system \begin{equation} \left\{ \begin{alignedat}{3} -Δu = & \, \frac{λf(x)}{(1-v)^2} & \quad \text{in} & \quadΩ\\ -Δv = & \, \frac{μg(x)}{(…
Regularity of stable solutions to quasilinear elliptic equations on Riemannian models
João Marcos do Ó, Rodrigo Clemente
We investigate the regularity of semi-stable, radially symmetric, and decreasing solutions for a class of quasilinear reaction-diffusion equations in the inhomogeneous context of R…