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

Let $\Omega$ be a bounded domain in $\mathbb R^n$ with smooth boundary. Assume that $u \in C^2(\bar \Omega) \cap H_0^1 (\Omega)$ be a strong solution to

\[  \Delta u = u^5 + 2 u^3 + 3 u \qquad \text{in}  \Omega, \]
with $u=0$ on $\partial \Omega$. Show that $u \equiv 0$ is the only solution.


Answers can be viewed only if
  1. The questioner was satisfied and accepted the answer, or
  2. The answer was disputed, but the judge evaluated it as 100% correct.
View the answer
The answer is accepted.
Join Matchmaticians Affiliate Marketing Program to earn up to 50% commission on every question your affiliated users ask or answer.