Abstract
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.
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