Existence of least energy positive and nodal solutions for a quasilinear Schrödinger problem with potentials vanishing at infinity |
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Prof. Giovany Figueiredo
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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. |