@article {ruiz2011, title = {Cluster solutions for the Schr{\"o}dinger-Poisson-Slater problem around a local minimum of the potential}, journal = {Rev. Mat. Iberoamericana}, volume = {27}, number = {1}, year = {2011}, month = {01}, pages = {253{\textendash}271}, publisher = {Real Sociedad Matem{\'a}tica Espa{\~n}ola}, url = {https://projecteuclid.org:443/euclid.rmi/1296828834}, author = {David Ruiz and Giusi Vaira} } @article {DAVENIA20115705, title = {Infinitely many positive solutions for a Schr{\"o}dinger{\textendash}Poisson system}, journal = {Nonlinear Analysis: Theory, Methods \& Applications}, volume = {74}, number = {16}, year = {2011}, pages = {5705 - 5721}, abstract = {

We are interested in the existence of infinitely many positive solutions of the Schr{\"o}dinger{\textendash}Poisson system -Δu+u+V(|x|)ϕu=|u|p-1u,x∈R3,-Δϕ=V(|x|)u2,x∈R3, where V(|x|) is a positive bounded function, 1\<p\<5 and V(r

}, keywords = {Non-autonomous Schr{\"o}dinger{\textendash}Poisson system, Perturbation method}, issn = {0362-546X}, doi = {https://doi.org/10.1016/j.na.2011.05.057}, url = {http://www.sciencedirect.com/science/article/pii/S0362546X11003518}, author = {Pietro d{\textquoteright}Avenia and Alessio Pomponio and Giusi Vaira} } @article {cerami2010positive, title = {Positive solutions for some non-autonomous Schr{\"o}dinger{\textendash}Poisson systems}, journal = {Journal of Differential Equations}, volume = {248}, number = {3}, year = {2010}, pages = {521{\textendash}543}, publisher = {Academic Press}, author = {Giovanna Cerami and Giusi Vaira} } @article {doi:10.1142/S0218202509003589, title = {Solutions of the Schr{\"o}dinger{\textendash}Poisson problem concentrating on spheres, part I: necessary conditions}, journal = {Mathematical Models and Methods in Applied Sciences}, volume = {19}, number = {05}, year = {2009}, pages = {707-720}, abstract = {

In this paper we study a coupled nonlinear Schr{\"o}dinger{\textendash}Poisson problem with radial functions. This system has been introduced as a model describing standing waves for the nonlinear Schr{\"o}dinger equations in the presence of the electrostatic field. We provide necessary conditions for concentration on sphere for the solutions of this kind of problem extending the results already known.

}, doi = {10.1142/S0218202509003589}, url = {https://doi.org/10.1142/S0218202509003589}, author = {Ianni, Isabella and Giusi Vaira} } @article {ianni2008concentration, title = {On concentration of positive bound states for the Schr{\"o}dinger-Poisson problem with potentials}, journal = {Advanced nonlinear studies}, volume = {8}, number = {3}, year = {2008}, pages = {573{\textendash}595}, publisher = {Advanced Nonlinear Studies, Inc.}, abstract = {

We study the existence of semiclassical states for a nonlinear Schr{\"o}dinger-Poisson system that concentrate near critical points of the external potential and of the density charge function. We use a perturbation scheme in a variational setting, extending the results in [1]. We also discuss necessary conditions for concentration.

}, doi = {10.1515/ans-2008-0305.}, author = {Ianni, Isabella and Giusi Vaira} }