Sign-changing solutions to a partially periodic nonlinear Schrödinger equation in domains with unbounded boundary
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DOI: 10.1007/s11784-018-0521-x
Abstract: We consider the problem $$\begin{aligned} -\Delta u+\left( V_{\infty }+V(x)\right) u=|u|^{p-2}u,\quad u\in H_{0} ^{1}(\Omega ), \end{aligned}$$-Δu+V∞+V(x)u=|u|p-2u,u∈H01(Ω),where $$\Omega $$Ω is either $$\mathbb {R}^{N}$$RN or a smooth domain in $$\mathbb {R} ^{N}$$RN with unbounded boundary, $$N\ge 3,$$N≥3,$$V_{\infty }>0,$$V∞>0,$$V\in… read more here.
Keywords: unbounded boundary; changing solutions; solutions partially; sign changing ... See more keywords