Uniqueness of Single Peak Solutions for a Kirchhoff Equation

We deal with the following singular perturbation Kirchhoff equation: - (& varepsilon;(2)a + & varepsilon;b integral(3)(R)|del u|(2)dy) Delta u + Q(y)u = |u|(p-1)u, u is an element of H-1 (R-3), where constants a, b, epsilon > 0 and 1 < p < 5. In this paper, we prove the uniqueness of the concentrated solutions under some suitable assumptions on a symptotic behaviors of Q(y)and its first derivatives by using a type of Pohozaev identity for a small enough epsilon.To some extent, our result exhibits a new phenomenon for a kind of Q(x) which allows for different orders in different directions