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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