About sharp conditions of uniqueness of large and existence of very singular solutions to semi-linear elliptic equations

There will be done a review of results about nonnegative solutions of semi-linear equations of diffusion-nonlinear absorption, which take infinite value on some subsets or all boundary of the domain under consideration: so called very singular and large solutions. For equations with absorption degenerating on the boundary of domain under consideration we establish new sharp necessary and sufficient conditions(criterion) of the existence of ( v.s.)solution with strong point singularity on the boundary. It is shown that these conditions are sufficient for uniqueness of large solution too. OPEN PROBLEM: whether these conditions are necessary for discussed uniqueness ?We are going to discuss the structure and main ideas of the proofs too.