## View abstract

### Session S18 - Recent progress in non-linear PDEs and their applications

Tuesday, July 20, 16:00 ~ 16:50 UTC-3

## Positive solutions to a nonlinear Choquard equation with symmetry

### Liliane Maia

#### University of Brasília (UnB), Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak2df1cce08d18792d21ff360681247509').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy2df1cce08d18792d21ff360681247509 = 'l&#105;l&#105;m&#97;&#105;&#97;' + '&#64;'; addy2df1cce08d18792d21ff360681247509 = addy2df1cce08d18792d21ff360681247509 + '&#117;nb' + '&#46;' + 'br'; var addy_text2df1cce08d18792d21ff360681247509 = 'l&#105;l&#105;m&#97;&#105;&#97;' + '&#64;' + '&#117;nb' + '&#46;' + 'br';document.getElementById('cloak2df1cce08d18792d21ff360681247509').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy2df1cce08d18792d21ff360681247509 + '\'>'+addy_text2df1cce08d18792d21ff360681247509+'<\/a>';

We will present some recent results on existence of positive solutions for a class of Choquard equations with potential decaying at a positive limit at infinity. The solutions found are invariant under the action of a closed subgroup of linear isometries of $\mathbb{R}^N$, provided the potential is invariant under the group action, and satisfies suitable decay assumptions. We investigate superlinear, linear and sublinear nonlinearities, and we take into account an arbitrary number of bumps. Our results in particular include the physical case.

Joint work with Benedetta Pellacci (Dipartimento di Matematica e Fisica,, Universit\a della Campania Luigi Vanvitelli'', Italy), and, Delia Schiera (Dipartimento di Matematica e Fisica, and Universit\a della Campania Luigi Vanvitelli'', Italy).