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We study the following class of double-phase nonlinear eigenvalue problems − div [φ(x, ∣∇u∣)∇u + ψ(x, ∣∇u∣)∇u] = λ f(x, u) in Ω, u = 0 on ∂Ω, where Ω is a bounded domain from RN with smooth boundary and the potential functions φ and ψ have (p1(x); p2(x)) variable growth. The main results of this paper are to prove the existence of a continuous spectrum consisting in a bounded interval in the near proximity of the origin, the fact that the multiplicity of every eigenvalue located in this interval is at least two and to establish the existence of infinitely many solutions for our problem. The proofs rely on variational arguments based on the Ekeland's variational principle, the mountain pass theorem, the fountain theorem and energy estimates. [ABSTRACT FROM AUTHOR]

In this paper we are concerned with the study of the spectrum for a class of eigenvalue problems driven by two non-homogeneous differential operators with different variable growth and an indefinite potential in the following form ... which is subjected to Dirichlet boundary condition. The proofs rely on variational arguments and they consist in finding two Rayleigh-type quotients, which lead us to an unbounded continuous spectrum on one side, and the nonexistence of the eigenvalues on the other. [ABSTRACT FROM AUTHOR]

In this article we study two problems, a nonlinear eigenvalue problem involving the p(x)-Laplacian and a subcritical boundary value problem for the same operator. We work on the variable exponent Sobolev spaces and use one of the variants of the Mountain-Pass Lemma. [ABSTRACT FROM AUTHOR]