# Thread: PDE - show that the principle eigenfunction is not sign changing

1. ## PDE - show that the principle eigenfunction is not sign changing

Studying for a test

a) show that the principle eigenfuntion is not sign changing
b) show all the other eigenfunctions are sign changing.

i'm not sure what this mean or what i meant by "princple"

can anone point me in the right direction?

2. The "principle eigenvalue" is the one that is largest in absolute value.

3. i have in my notes that all of the eigenvalues are positive
wouldn't all of the eigenfunctions also be positive?

my professor mentioned something in class about the fact that

Int(u_1*u_m*rho dx)=0

>>> u_1>0, rho>0

>>> u_m must be sign changing

i think that what he said is pretty much all of it, but i really don't know what it means and i don't have anyone around that is in pde with me to ask... i have a test on friday... HELP

i'm not sure why these questions are relevant
i am under the impression that if something is sign changing it will cancel to zero when you comupet the integral, but then the whole integral would be zero....
and i always get confused when i get a lot of zeros, because it normally means i have made a mistake...