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math.AP2015★ 1 cited
Boundary concentrations on segments
Weiwei Ao, Hardy Chan, Juncheng Wei
We consider the following singularly perturbed Neumann problem \begin{eqnarray*} \ve^2 Δu -u +u^p = 0 \, \quad u>0 \quad {\mbox {in}} \quad Ω, \quad {\partial u \over \partial ν}=0…
math.AP2015
Nondegeneracy of nonradial sign-changing solutions to the nonlinear Schrödinger equations
Weiwei Ao, Monica Musso, Juncheng Wei
We prove that the non-radial sign-changing solutions to the nonlinear Schrödinger equation \begin{equation*} Δu-u+|u|^{p-1}u=0 \mbox{ in }\R^N, \quad u \in H^1 (\R^N ) \end{equatio…