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Wednesday June 6, 2018 (11 am, Sala di Rappresentanza)

Carlo Mercuri

(Swansea University)

On a class of nonlinear Schrödinger-Poisson systems

involving a nonradial charge density

(Swansea University)

On a class of nonlinear Schrödinger-Poisson systems

involving a nonradial charge density

Abstract: In the spirit of the classical work of P. H. Rabinowitz [ZAMP '92] we will discuss about existence

of mountain-pass solutions and least energy solutions to the nonlinear Schrödinger-Poisson system

of mountain-pass solutions and least energy solutions to the nonlinear Schrödinger-Poisson system

`\{` | `-\Delta u+u+
\rho(x) \phi u=|u|^{p-1}u, \quad x \in
\mathbb{R}^3,` `-\Delta \phi= \rho(x)u^2, \quad x \in \mathbb{R}^3,` |

under different assumptions on `\rho: \mathbb{R}^3 \to \mathbb{R}_+`
at infinity. A singular perturbation of the above problem will be also
considered in various functional settings which are suitable for both
variational and perturbation methods.