I'm trying to solve the eigenvalue problem
$$(1+x^2+y^2)\left[(1+x^2)\frac{\partial^2f}{\partial x^2}+(1+y^2)\frac{\partial^2f}{\partial y^2}+2xy \frac{\partial^2f}{\partial x \partial y}+2x\frac{\partial f}{\partial x}+2y\frac{\partial f}{\partial y}\right]=\lambda f$$ in the region $$(1,\infty)\times(1,\infty)$$ with Dirichlet boundary condition $$f=0$$ in the frontier. I suppose that the problem can be numerically treated but I don't know how to do it. I need some help.