About Theorem 3.1.1, Remark 3.1.3 state that the strong maximum principle means a better results. I find the strong maximum principle from Evans' book which is in 3th picture below. The operator $L$ is $$ Lu = -a^{ij}u_{ij} +b^i u_i +cu $$ where $u_i =\partial_i u$. But seemly, the term $F(u,t)$ can't be deal by $cu$. Therefore, I want to know which strong maximum principle I should use ?
PS: I find a new strong maximum principle in The Ricci flow Techniques and Applications Part II: Analytic Aspects, which is contained in 4th 5th pictures below. But seemly, it also can't deal the $F(u,t)$. In fact, after finding book, I feel the Remark 3.1.3 maybe wrong. But I am not sure.
