Derivation of Green's function in Evans' PDE book. In the book of Evans, on page 34 equation $(25)$ isn't the RHS should be minus what is written there, I mean he uses the fact that $\Delta \Phi(y-x) = \delta(y-x)$ on $U$, and he moves the second term in eq. $(24)$ to the RHS.
If this is not the case then how did he derive equation $(25)$?
The book has a preview on pages 33-34.
https://books.google.co.il/books?id=Xnu0o_EJrCQC&printsec=frontcover#v=onepage&q&f=false

The following is Theorem 1 at page 23 in Evans' book

Let $u = \Phi * f$, then $u \in C^2$ and $\color{red}{-}\Delta u = f.$

Then one adopts the notation $$-\Delta \Phi = \delta_0,$$ thanks to which we can formally compute $$-\Delta u = (-\Delta \Phi) * f = \int \delta(x - y)f(y) = f(x).$$
This should fix your sign problem.
