How does one go about solving a two dimensional (or more) homogeneous helmholtz equation with a variable coefficient, i.e.
u(x,y) + u(x,y)*f(x,y) = 0
Where in the standard Helmholtz equation, f(x,y) = k (constant). Knowing some boundary conditions. I am at a loss as to what method to even use, having tried separation of variables, green's functions, method of characteristics. Any hints? Can this equation even be solved?