Workshop on Pdes 2022 - Figueiredo

Existence of  least energy positive and nodal solutions for a quasilinear Schrödinger  problem with potentials vanishing at infinity

Prof. Giovany Figueiredo
Universidade de Brasília

Date: 16th February 13:30 pm - 14:15 pm (UTC -3) Link: PPGM/UFSCar Youtube channel

Abstract: In this talk we prove the  existence  of   at least two nontrivial solutions for a  class of quasilinear problems with two nonnegative and continuous potentials.  Thanks to the geometries these potentials, we are able to prove compact embeddings in some weighted Sobolev spaces and  by a minimization argument   we find   a positive and a nodal (or sign-changing) (weak) solution with  two nodal domains or that changes sign exactly once in RN for such problems.  The  nonlinearity in this problem satisfies suitable growth and monotonicity conditions which allow this result  to complement classical results due to Jia-quan Liu, Ya-qi Wang and Zhi-Qiang Wang.