By using the Leray-Schauder continuation theorem, we establish the existence of solutions for m -point boundary value problems on a half-line x ″ ( t ) + f ( t , x ( t ) , x ′ ( t ) ) = 0 , 0 < t < + ∞ , x ( 0 ) = ∑ i = 1 m − 2 α i x ( η i ) , lim ⁡ t → + ∞ x ′ ( t ) = 0 , where α i ∈ R , ∑ i = 1 m − 2 α i ≠ 1 and 0 < η 1 < η 2 < ⋯ < η m − 2 < + ∞ are given.