Classification of Radial Solutions to the Emden-fowler Equation on the Hyperbolic Space
نویسنده
چکیده
We study the Emden-Fowler equation −∆u = |u|u on the hyperbolic space H . We are interested in radial solutions, namely solutions depending only on the geodesic distance from a given point. The critical exponent for such equation is p = (n + 2)/(n − 2) as in the Euclidean setting, but the properties of the solutions show striking differences with the Euclidean case. While the papers [23, 4] consider finite energy solutions, we shall deal here with infinite energy solutions and we determine the exact asymptotic behavior of wide classes of finite and infinite energy solutions.
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