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math.AP2024
Steady-states of the Gierer-Meinhardt system in exterior domains
Marius Ghergu, Jack McNicholl
We discuss the existence and nonexistence of solutions to the steady-state Gierer-Meinhardt system $$ \begin{cases} \displaystyle -Δu=\frac{u^p}{v^q}+λρ(x) \,, u>0 &\quad\mbox{ in…
math.AP2024
Asymptotically homogeneous solutions of the supercritical Lane-Emden system
Louis Dupaigne, Hatem Hajlaoui, Marius Ghergu
We consider the Lane-Emden system-u = |v| p-1 v,-v = |u| q-1 u in R d. When p q 1, it is known that there exists a positive radial stable solution (u, v) C…