| Abstract: |
| We study the nonlocal scalar field equations with a vanishing parameter $\epsilon$.
For $\epsilon>0$ small, we prove the existence of a ground state solution and show that any positive solution is a classical solution and radially symmetric and symmetric decreasing. We also obtain the decay rate of solution at infinity. Next, we characterize the asymptotic behavior of ground state solutions and using this we prove the {\textit local uniqueness} of solution. |
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