Multiplicity of Solutions for Some $p(x)$-Biharmonic Problem
by
Abdeljabbar Ghanmi
Vol. 16 No. 4 (2021) P.401~P.421
DOI: | https://doi.org/10.21915/BIMAS.2021406 |
| 10.21915/BIMAS.2021406 |
ABSTRACT
This paper deals with the study of some class of non-homogeneous problems involving
the $p(x)$-biharmonic operator. Using direct variational methods, the existence of nontrivial
solution is obtained. The multiplicity of solutions is obtained by combining Ekeland’s
variational principle with the Mountain pass theorem. Finally, the Fountain theorem is
applied to prove the existence of infinetely many solutions for the given problem.
KEYWORDS
p(x)-Laplace operator, Variational methods, Variable exponents, Ekeland's variational
principle, Mountain pass theorem, Fountain theorem
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 31B30, 35J35
MILESTONES
Received: 2021-12-09
Revised :
Accepted: 2021-12-21
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