Non-autonomous Eigenvalue Problems with Variable (p1,p2)-Growth

Abstract

We are concerned with the study of a class of non-autonomous eigenvalue problems driven by two non-homogeneous differential operators with variable (p1,p2){(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.

Keywords

• non-autonomous eigenvalue problem
• continuous spectrum
• non-homogeneous differential operator
• variable exponent
• 35p30
• 49r05
• 58c40