Self adjoint differential equation?

[vivek.iitd]

Hello everyone, could you please make me understand, what are self-adjoint equations? and how can we convert a differential equation into a self-adjoint form?

Thank you.

[hunt_mat]

Let T by the differential equation and denote an inner product by:

(v,Tu)=\int vTudx

If

(T^{\star}v,u)=(v,Tu)

Then the differential operator is self adjoint.