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In this paper, we are concerned with the uniqueness and the non-degeneracy ofpositive radial solutions for a class of semilinear elliptic equations. Usingdetailed ODE analysis, we extend previous results to cases where nonlinearterms may have sublinear growth. As an application, we obtain the uniquenessand the non-degeneracy of ground states for modified Schr\"odinger equations.

A note on the uniqueness and the non-degeneracy of positive radial solutions for semilinear elliptic problems and its application