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We study the general semilinear second-order ODE 𝑢+𝑔(𝑡,𝑢,𝑢)=0 under different two-point boundary conditions. Using the method of upper and lower solutions, we obtain an existence result. Moreover, under a growth condition on 𝑔, we prove that the set of solutions of 𝑢+𝑔(𝑡,𝑢,𝑢)=0 is homeomorphic to the two-dimensional real space.