The sign-changing solutions and ground states for planar Schrödinger–Newton system with an exponential critical growth
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DOI: 10.1063/5.0006482
Abstract: In this paper, we study the planar Schrodinger–Newton system with a Coulomb potential where the nonlinearity is super-linear at zero and exponential critical at infinity. With a weaker condition than the Nehari type monotonic condition,… read more here.
Keywords: ground states; sign changing; newton system; exponential critical ... See more keywords
Multiplicity and Concentration Results for a Magnetic Schrödinger Equation With Exponential Critical Growth in ℝ2
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DOI: 10.1093/imrn/rnaa074
Abstract: In this paper we study the following nonlinear Schrödinger equation with magnetic field $$\begin{align*} \left(\frac{\varepsilon}{i}\nabla-A(x)\right)^{2}u+V(x)u=f(| u|^{2})u,\quad x\in\mathbb{R}^{2}, \end{align*}$$where $\varepsilon>0$ is a parameter, $V:\mathbb{R}^{2}\rightarrow \mathbb{R}$ and $A: \mathbb{R}^{2}\rightarrow \mathbb{R}^{2}$ are continuous potentials, and $f:\mathbb{R}\rightarrow \mathbb{R}$ has… read more here.
Keywords: dinger equation; critical growth; exponential critical; multiplicity concentration ... See more keywords