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.
Existence and Multiplicity Results for Some Scalar Fields Equations / Cerami, Giovanna (PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS). - In: Analysis and Topology in Nonlinear Differential Equations: A Tribute to Bernhard Ruf on the Occasion of his 60th Birthday / [a cura di] Djairo G de Figueire; doJoão Marcos do Ó; Carlos Tomei. - STAMPA. - Cham : Birkhäuser, 2014. - ISBN 978-3-319-04312-8. - pp. 207-230 [10.1007/978-3-319-04214-5_12]
Existence and Multiplicity Results for Some Scalar Fields Equations
Cerami, Giovanna
2014-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
