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Surface Gap Soliton Ground States for the Nonlinear Schrödinger Equation
Surface Gap Soliton Ground States the Nonlinear Schrö dinger Equation
2010/11/1
We consider the nonlinear Schr\"{o}dinger equation $(-\Delta +V(x))u = \Gamma(x) |u|^{p-1}u$, $x\in \R^n$ with $V(x) = V_1(x) \chi_{\{x_1>0\}}(x)+V_2(x) \chi_{\{x_1<0\}}(x)$ and $\Gamma(x) = \Gamma_1(...
Uniqueness and Nondegeneracy of Ground States for $(-\Delta)^s Q + Q - Q^{\alpha+1} = 0$ in $\R$
Uniqueness Nondegeneracy of Ground States
2010/9/1
We prove uniqueness of ground state solutions Q = Q(|x|) > 0 for the nonlinear equation (−)sQ + Q − Q +1 = 0 in R,where 0 < s < 1 and 0 < < 4s 1−2s for s < 1/2 and 0 < < 1 for s...