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Spectrum in an unbounded interval for a class of nonhomogeneous differential operators

The present paper deals with the spectrum of a nonhomogeneous problem involving variable exponents on an exterior domain in ℝN. The existence of two positive real numbers λ0 and λ1, is established satisfying the condition λ0⩽λ1, such that the problem has no eigenvalue in the interval (0, λ0) while any number in the interval [λ1, ∞) is an eigenvalue.