Nonlinear eigenvalue problems for a biharmonic operator in Orlicz–Sobolev spaces

Abstract In this paper, we study a higher‐order Laplacian operator in the framework of Orlicz–Sobolev spaces, the biharmonic g ‐Laplacian where , with being an N ‐function. This operator is a generalization of the so‐called bi‐harmonic Laplacian . Here, we also establish basic functional properties of , which can be applied to existence results. Afterwards, we study the eigenvalues of , which depend on normalization conditions, due to the lack of homogeneity of the operator. Finally, we study different nonlinear eigenvalue problems associated to and we show regimes where the corresponding spectrum concentrates at 0, or coincide with .