Uniqueness of positive solutions of Δu−u+up=0 in Rn

Stability of solitary waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities

“…Since the positive solution R 0 of (4.7) is unique [6], then, as in Lemma 5(b) R 1 , R 2 → R 0 uniformly. Therefore,…”

“…Throughout this paper, we make the following assumptions on V : 6) where V (i) is the ith derivative of V . We note that these assumptions are consistent with the electron density induced by the preliminary beam.…”

Semilinear problems on the half space with a hole

“…Kwong [11] proved that the positive solution of (1 R JV) is unique up to translations. Throughout this article denote by u the unique solution of equation (In.AT) which attains its maximum at 0, / R jv \u\ p = 1, ||u|| = a, and satisfies (1-1).…”

Quantitative properties on the steady states to a Schrödinger–Poisson–Slater System

“…and its generalizations, we only mention the paper [11] here. For the SPS system, the difficulty mainly stems from the nonlocal term, for which requires the global information of the solutions always.…”