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and Applied Analysis 3 (ii) Let p1, p2 ∈ C+(Ω) be given such that p1(x) ≤ p2(x) for any x ∈ Ω then Lp2(x)(Ω) is continuously embedded into Lp1(x)(Ω). Proposition 2 (see [11, 32, 33]). Let ρ (u) = ∫ Ω |u|p(x) dx, ∀u ∈ Lp(x) (Ω) . (8)

Qualitative Properties of Nonnegative Solutions for a Doubly Nonlinear Problem with Variable Exponents