Existence Results For Semilinear Problems in the Two Dimensional   Hyperbolic Space Involving Critical Growth
  We consider semilinear elliptic problems on two-dimensional hyperbolic space involving critical growth. We first establish the Palais-Smale(P-S) condition and using (P-S) condition we obtain existence of solutions. In addition, we also explore existence of infinitely many sign changing solutions as well. 
Debabrata Karmakar, Debdip Ganguly
math.AP