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In this paper, we consider a (ϕ 1 , ϕ 2) -Laplacian system as follows: { Δ ϕ 1 (Δ u (t − 1)) + ∇ u F (t , u (t) , v (t)) = 0 , Δ ϕ 2 (Δ v (t − 1)) + ∇ v F (t , u (t) , v (t)) = 0 , where F (t , u (t) , v (t)) = − K (t , u (t) , v (t)) + W (t , u (t) , v (t)) is T-periodic in t. By using the mountain pass theorem, we obtain that the (ϕ 1 , ϕ 2) -Laplacian system has at least one periodic solution if W is asymptotically (p , q) -linear at infinity. Our results improve and extend some known works. [ABSTRACT FROM AUTHOR]

In this paper, a class of nonlinear ψ-Hilfer fractional integrodifferential coupled systems on a bounded domain is investigated. The existence and uniqueness results for the coupled systems are proved based on the contraction mapping principle. Moreover, the Ulam–Hyers–Rassias, Ulam–Hyers, and semi-Ulam–Hyers–Rassias stabilities to the initial value problem are obtained. [ABSTRACT FROM AUTHOR]