53 citations · 307 across the 52 of their papers we have counts for
6 papers · 1 filter
A semilinear elliptic equation with competing powers and a radial potential
M. Musso, J. Pimentel
We verify the existence of radial positive solutions for the semi-linear equation $$ -\,Δu=u^{p}\,-\,V(y)\,u^{q},\,\quad\quad u>0,\quad\quad\mbox{ in }\mathbb{R}^N$$ where $N\geq 3…
High energy sign-changing solutions for Coron's problem
Shengbing Deng, Monica Musso
We study the existence of sign changing solutions to the following problem $$ (P) \quad \quad \quad \left\{ \begin{array}{ll} Δu+|u|^{p-1}u=0 \quad & {\rm in} \quad Ω_ε; u=0 \quad…
Geometry driven Type II higher dimensional blow-up for the critical heat equation
Manuel del Pino, Monica Musso, Juncheng Wei
We consider the problem v_t & = Δv+ |v|^{p-1}v \quad\hbox{in }\ Ω\times (0, T), v & =0 \quad\hbox{on } \partial Ω\times (0, T ) , v& >0 \quad\hbox{in }\ Ω\times (0, T) . In a domai…
Bubbling solutions for Moser-Trudinger type equations on compact Riemann surfaces
Pablo Figueroa, Monica Musso
We study an elliptic equation related to the Moser-Trudinger inequality on a compact Riemann surface , $$ Δ_g u+λ\Biggl(ue^{u^2}-{1\over |S|} \int_S ue^{u^2} dv_g\Biggl)=0,\…
Embedded tori with prescribed mean curvature
Paolo Caldiroli, Monica Musso
We construct a sequence of compact, oriented, embedded, two-dimensional surfaces of genus one into Euclidean 3-space with prescribed, almost constant, mean curvature of the form $H…
Infinite time blow-up for the 3-dimensional energy critical heat equation
Manuel del Pino, Monica Musso, Juncheng Wei
We construct globally defined in time, unbounded positive solutions to the energy-critical heat equation in dimension three $$ u_t = Δu + u^5 , \quad {\mbox {in}} \quad \R^3 \times…