Eigenvalue problems for anisotropic elliptic equations: An Orlicz–Sobolev space setting

The paper studies a class of anisotropic eigenvalue problems involving an elliptic, nonhomogeneous differential operator on a bounded domain from RNRN with a smooth boundary. Some results regarding the existence or non-existence of eigenvalues are obtained. In each case the competition between the growth rates of the anisotropic coefficients plays an essential role in the description of the set of eigenvalues.