Existence and multiplicity results for double phase problem

By variational method, we obtain various existence and multiplicity results for the following double phase problem{−div(|∇u|p−2∇u+a(x)|∇u|q−2∇u)=f(x,u)in Ω,u=0on ∂Ω. In particular, we find a sign-changing ground state solution. Some properties of double phase operator are also obtained....

Full description

Saved in:
Bibliographic Details
Published inJournal of Differential Equations Vol. 265; no. 9; pp. 4311 - 4334
Main Authors Liu, Wulong, Dai, Guowei
Format Journal Article
LanguageEnglish
Published Elsevier Inc 05.11.2018
Subjects
Double phase problems
Musielak–Orlicz spaces
Sign-changing solution
35D05
03H10
Sign-changing solution
Double phase problems
Musielak–Orlicz spaces
35J60
Online AccessGet full text

Cover

More Information
Summary:By variational method, we obtain various existence and multiplicity results for the following double phase problem{−div(|∇u|p−2∇u+a(x)|∇u|q−2∇u)=f(x,u)in Ω,u=0on ∂Ω. In particular, we find a sign-changing ground state solution. Some properties of double phase operator are also obtained.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2018.06.006