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We consider semilinear elliptic problems on two-dimensional hyperbolic spaceinvolving critical growth. We first establish the Palais-Smale(P-S) conditionand using (P-S) condition we obtain existence of solutions. In addition, wealso explore existence of infinitely many sign changing solutions as well.

Existence Results For Semilinear Problems in the Two Dimensional Hyperbolic Space Involving Critical Growth