In the Book Evans, Partial Differential Equations, 2010, Theorem 3, p. 319, we have that there's an $\gamma \geq 0$ such that for each $\mu \geq \gamma$ and each function $f \in L^2(\Omega)$, there's a unique weak solution in $H^1_0(\Omega)$ of the equatin $$ (P) \begin{cases} L(u) + \mu u = f, \Omega \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,u = 0, \partial \Omega. \end{cases} $$ Essentially, we the the $\gamma$ for which the associated bilinear form is coercive.
I'm wondering if the solution depends on the $\mu$ I take, that is, given $\mu_1, \mu_2 \geq \gamma$ and $u_1,u_2$ the respective weak solutions of $(P)$, we have $u_1 = u_2$?