Hamiltonian elliptic systems: a guide to variational frameworks
Hamiltonian elliptic systems: a guide to variational frameworks
Consider a Hamiltonian elliptic system of type \left\{ \begin{array}{ll} -\Delta u=H_{v}(u,v) & \text{ in } \Omega\\ -\Delta v=H_{u}(u,v) & \text{ in } \Omega\\ u,v=0 & \text{ on } \partial \Omega \end{array} \right. where H is a power-type nonlinearity, for instance H(u,v)= |u|^{p+1}/(p+1)+|v|^{q+1}/(q+1) , having subcritical growth, and \Omega is a …