Speaker
Alberto Saldaña, Universidad Nacional Autónoma de México
Abstract
We study a nonlinear indefinite equation in the whole space, where the right hand side is a power nonlinearity multiplied by a coefficient Q exhibiting a sharp change of sign. Our aim is to understand how the exponent of the nonlinearity and the geometry and the topology of the positivity set of Q influence the qualitative properties of solutions. We review some recent results on uniqueness and multiplicity, describe the shape of solutions, and analyze concentration phenomena arising in some regimes. This talk is based on joint works with Mónica Clapp, Jorge Faya, Víctor Hernández-Santamaría, Cristian Morales-Encinos, Angela Pistoia, Delia Schiera, Mayra Soares, and Andrzej Szulkin.
Alberto Saldaña, Universidad Nacional Autónoma de México
Abstract
We study a nonlinear indefinite equation in the whole space, where the right hand side is a power nonlinearity multiplied by a coefficient Q exhibiting a sharp change of sign. Our aim is to understand how the exponent of the nonlinearity and the geometry and the topology of the positivity set of Q influence the qualitative properties of solutions. We review some recent results on uniqueness and multiplicity, describe the shape of solutions, and analyze concentration phenomena arising in some regimes. This talk is based on joint works with Mónica Clapp, Jorge Faya, Víctor Hernández-Santamaría, Cristian Morales-Encinos, Angela Pistoia, Delia Schiera, Mayra Soares, and Andrzej Szulkin.