Abstract. In this paper, we investigate a class of problems with Neumann boundary data in Musielak--Orlicz--Sobolev spaces $W^1L_M(\Omega )$. We prove the existence of infinitely many weak solutions under some hypotheses. We also provide some particular cases and a concrete example in order to illustrate the main results. Our results are an improvement and generalization of the relative results [1].

DOI: 10.14232/actasm-020-161-9

AMS Subject Classification (1991): 35A15, 58E05; 35J60

Keyword(s): Musielak--Sobolev spaces, Kirchhoff type problem, variational methods, critical point theory

received 11.4.2020, revised 15.6.2020, accepted 28.9.2020. (Registered under 411/2020.)