Uniqueness Results and Asymptotic Behaviour of Nonlinear Schrödinger-Kirchhoff Equations

In this paper, we first study the uniqueness and symmetry of solution of nonlinear Schrodinger-Kirchhoff equations with constant coefficients. Then, we show the uniqueness of the solution of nonlinear Schrodinger-Kirchhoff equations with the polynomial potential. In the end, we investigate the asymptotic behaviour of the positive least energy solutions to nonlinear Schrodinger-Kirchhoff equations with vanishing potentials. The vanishing potential means that the zero set of the potential is non-empty. The uniqueness results of Schrodinger equations and the scaling technique are used in our proof. The elliptic estimates and energy analysis are applied in the proof of the asymptotic behaviour of the above Schrodinger-Kirchhoff-type equations.

Automated summary

In this paper, we investigate the uniqueness and symmetry of solutions to nonlinear Schrodinger-Kirchhoff equations with constant coefficients, demonstrate the uniqueness of solutions to nonlinear Schrodinger-Kirchhoff equations with polynomial potential, and analyze the asymptotic behavior of positive least energy solutions to nonlinear Schrodinger-Kirchhoff equations with vanishing potentials.