Existence of three weak solutions for fourth-order Leray–Lions problem with indefinite weights

Abstract

In this paper, we establish the existence of at least three weak solutions for the fourth-order problem with indefinite weights involving the Leray–Lions operator with nonstandard growth conditions. We generalize the result obtained by Kefi et al. [On the fourth-order Leray–Lions problem with indefinite weight and nonstandard growth conditions. Bull Math Sci. 2021;DOI:10.1142/S1664360721500089]. The proof of our main result uses variational methods and the critical theorem of Bonanno and Marano [On the structure of the critical set of nondifferentiable functions with a weak compactness condition. Appl Anal. 2010;89:1–10].