The exercise is given by
as an eigenvalue problem where
( denotes the sobolev space on the open intervall (0,1). For those who don't know that just assume V is a subspace of functions on this intervall with boundary values of 0 that have the first order derivative.)
I don't know how to begin this. I have to find something in the way where A is a given matrix, b is a given vector and x the solution that has to be found. But how can I do this? Or even better I just have to find a matrix which (absolute) greatest eigenvalue determines this value?
I tried partial integration but it really leads me nowhere... Does anyone have a hint how to solve this?