Multiplicity of solutions for a non-local problem with indefinite weights

Abstract

In this manuscript, we show that at least three weak solutions exist for a non-local $p(x)$-biharmonic problem. The variational method and the critical theorem of Bonanno and Marano (Appl. Anal. 89 (2010), 1–10) are used to prove our main result.

KEYWORDS:

• Critical theorem
• generalized Sobolev space
• variable exponent

MATHEMATICS SUBJECT CLASSIFICATION (2020):

• 35J20
• 35J60
• 35G30
• 35J35
• 46E35

The authors extend their appreciation to the Deanship of Scientific Research at Northern Border University, Arar, KSA for funding this research work through the project number ‘NBU-FFR-2023-0012’. The fourth author acknowledges the support of the Deanship of Science Research (DSR) at King Abdulaziz University, Jeddah.

Disclosure statement

No potential conflict of interest was reported by the author(s).