We are not able to resolve this OAI Identifier to the repository landing page. If you are the repository manager for this record, please head to the Dashboard and adjust the settings.
We study the mixed dispersion fourth order nonlinear Schr\"odinger equation \begin{equation*} %\tag{\protect{4NLS}}\label{4nls} i \partial_t \psi -\gamma \Delta^2 \psi +\beta \Delta \psi +|\psi|^{2\sigma} \psi =0\ \text{in}\ \R \times\R^N, \end{equation*} where γ,σ>0 and β∈R. We focus on standing wave solutions, namely solutions of the form ψ(x,t)=eiαtu(x), for some α∈R. This ansatz yields the fourth-order elliptic equation \begin{equation*} %\tag{\protect{*}}\label{4nlsstar} \gamma \Delta^2 u -\beta \Delta u +\alpha u =|u|^{2\sigma} u. \end{equation*} We consider two associated constrained minimization problems: one with a constraint on the L2-norm and the other on the L2σ+2-norm. Under suitable conditions, we establish existence of minimizers and we investigate their qualitative properties, namely their sign, symmetry and decay at infinity as well as their uniqueness, nondegeneracy and orbital stability
Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.