In this paper the results of some researches concerning Scalar Field Equations are summarized. The interest is focused on the question of existence and multiplicity of stationary solutions, so the model equation −Δu+a(x)u=|u|p−1uinRN is considered. The difficulties and the ideas introduced to face them as well as some well known results are discussed. Some recent advances concerning existence and multiplicity of multi-bump solutions are described in more detail.
|Titolo:||Existence and Multiplicity Results for Some Scalar Fields Equations|
|Titolo del libro:||Analysis and Topology in Nonlinear Differential Equations: A Tribute to Bernhard Ruf on the Occasion of his 60th Birthday|
|Data di pubblicazione:||2014|
|Digital Object Identifier (DOI):||10.1007/978-3-319-04214-5_12|
|Appare nelle tipologie:||2.1 Contributo in volume (Capitolo o Saggio)|