Abstract:

A class of asymptotically linear elliptic equations with Hardy potential and critical parameter is considered. For general bounded domain Ω, there is no nontrivial solution in space H¹₀ (Ω) for this kind of equation (see  reference［1］). The existence of non-trivial solutions  are proved in a new Sobolev-Hardy space with the technique of Morse theory.

Key words: Hardy potential; critical parameter; asymptotically linear; Morse theory