Polyharmonic inequalities with nonlocal terms

We study the existence and non-existence of classical solutions for inequalities of type±Δmu≥(Ψ(|x|)⁎up)uq in RN(N≥1). Here, Δm(m≥1) is the polyharmonic operator, p,q>0 and ⁎ denotes the convolution operator, where Ψ>0 is a continuous non-increasing function. We devise new methods to deduce th...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 296; pp. 799 - 821
Main Authors Ghergu, Marius, Miyamoto, Yasuhito, Moroz, Vitaly
Format Journal Article
LanguageEnglish
Published Elsevier Inc 25.09.2021
Subjects
Liouville type results
Nonlocal terms
Poly-superharmonic property
Polyharmonic inequalities
35J30
Poly-superharmonic property
Polyharmonic inequalities
Nonlocal terms
35A23
35G50
35B53
Liouville type results
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Summary:We study the existence and non-existence of classical solutions for inequalities of type±Δmu≥(Ψ(|x|)⁎up)uq in RN(N≥1). Here, Δm(m≥1) is the polyharmonic operator, p,q>0 and ⁎ denotes the convolution operator, where Ψ>0 is a continuous non-increasing function. We devise new methods to deduce that solutions of the above inequalities satisfy the poly-superharmonic property. This further allows us to obtain various Liouville type results. Our study is also extended to the case of systems of simultaneous inequalities.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2021.06.019