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On a critical Hamiltonian system with Neumann boundary conditions by Pistoia, Angela; Schiera, Delia is a scholarly article available to read on EtoBox.

What is On a critical Hamiltonian system with Neumann boundary conditions about?

We consider the Hamiltonian system with Neumann boundary conditions: \[ -\Delta u + \mu u=v^{q }, \quad -\Delta v+ \mu v=u^{p} \quad \text{ in $\Omega$}, \qquad u, v >0 \quad \text{ in $\Omega$,} \qquad \partial_\nu u= \partial_\nu v=0 \quad \text{ on $\partial \Omega$, } \] where $\mu >0$ is a parameter and $\Omega$ is a smooth bounded domain in $\mathbb R^N .$ When $(p, q)$ approaches from below the critical hyperbola $N/(p+1) + N/(q+1)=N-2$, we build a solution which blows-up at a boundary point where the mean curvature achieves its minimum and negative value.

Author

Pistoia, Angela; Schiera, Delia

Published

2024

Language

EN