# Uniqueness of solutions of the elliptic equation $\Delta u = u^5 + 2 u^3 + 3 u$

\[ \Delta u = u^5 + 2 u^3 + 3 u \qquad \text{in} \Omega, \]

with $u=0$ on $\partial \Omega$. Show that $u \equiv 0$ is the only solution.

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