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Infinitely many solutions for polyharmonic equations of p ( x )‐Laplace type
Author(s) -
Bae JungHyun,
Kim JaeMyoung
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6656
Subject(s) - mathematics , laplace transform , class (philosophy) , type (biology) , mathematical analysis , ecology , artificial intelligence , computer science , biology
We show the existence of infinitely many weak solutions to a class of quasilinear elliptic p ( x )‐polyharmonic Kirchhoff equations via the mountain pass principle without the (AR) condition. Furthermore, we obtain infinitely many solutions to this equation based on the genus theory, introduced by Krasnoselskii and the abstract critical point theorem (a variant of Ljusternik‐Schnirelman theory) under Cerami condition.