Abstract
We give an analytical and topological proof of the uniqueness of the ground state of the nonlinear Schrödinger equation defined on the Hyperbolic space ℍd when the power type nonlinearity has H1(ℍd)-subcritical exponent (1<p<1+4∕(d−2) for d≥3 and 1<p<+∞ for d=2) and the phase λ is positive. Differently from what it is available in the literature, we use the polar model of ℍd and we do not take advantage of the dual Euclidean problem. Our proof of uniqueness uses the shooting method, some new monotonicity formulas and the geometry of the potential energy.
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