Infinitely Many Periodic Solutions for Variable Exponent Systems

Abstract

We mainly consider the system −Δp(x)u=f(v)+h(u) in ℝ, −Δq(x)v=g(u)+ω(v) in ℝ, where 1<p(x),q(x)∈C1(ℝ) are periodic functions, and −Δp(x)u=−(|u′|p(x)−2u′)′ is called p(x)-Laplacian. We give the existence of infinitely many periodic solutions under some conditions.