Non-autonomous Eigenvalue Problems with Variable ( p 1 , p 2 )-Growth
Sami Baraket, Souhail Chebbi, Nejmeddine Chorfi, Vicenţiu D. Rădulescu · Advanced Nonlinear Studies · 2017
Abstract We are concerned with the study of a class of non-autonomous eigenvalue problems driven by two non-homogeneous differential operators with variable ( p 1 , p 2 ) {(p_{1},p_{2})} -growth. The main result of this paper establishes the existence of a continuous spectrum consisting in an unbounded interval and the nonexistence of eigenvalues in a neighbourhood of the origin. The abstract results of this paper are described by two Rayleigh-type quotients and the proofs rely on variational arguments.