... t for each x ∈ Rn, and f is continuous in x for each t ∈ 0,T, such that |ft, x|≤gt for t, x ∈ 0,T × Rn,whereg· ∈ L20,T, andlet Ik: Rn→ Rnbe continuous functions for ... CRn,Rn. Under certain conditions on G, f,andIku for k 1, 2, ,p, we prove an existence result for E1.2.2. Antiperiodic Problem for Differential Equations in RnLet |·|be the norm in ... ΔutiIiuti,fori 1, 2, ,p.ThenuPCJ≤1 −12α−1⎡⎣12δ √T2T0us2ds1/2⎤⎦. 3.1Proof. By assumption, we have utu0t0usds for t ∈ 0,t1,andut...