Recently I received a problem from two different people that want to convert an equation to a Sturm Liouville problem then solve it with boundary conditions. but I'm wondering how the problem could convert to it. there is a delta sign in it but what surprised me that I never see it in a Sturm-Liouville problem before. here is the question:
$\Delta{u}=xy^2+x^2y \qquad \qquad \qquad -1<x<1 \quad\&\quad0<y<1 $
$ u(-1,y)=u(1,y)+y^2$
$u_x(-1,y)=u_x(1,y)+y$
$u_x(x,0)=x^2$
$u(x,1)+u_y(x,1)=x$
now my question is: is this problem is correct or just a miss typing(what do you think what was the original problem) if this problem is ok please give me a hint to solve it. thank you all and any help would be appreciated.