On the fourth-order Leray-Lions problem with indefinite weight and nonstandard growth conditions

We prove the existence of at least three weak solutions for the fourth-order problem with indefinite weight involving the Leray-Lions operator with nonstandard growth conditions. The proof of our main result uses variational methods and the critical theorem of Bonanno and Marano (Appl. Anal. 89 (2010), 1-10).