Abstract:
A boundary value problem for a nonlinear ordinary differential equation of the fourth order is considered. Using the Green function, the boundary value problem is reduced to an equivalent integral equation. In the sublinear case, after identifying the properties of the Green function necessary for further study, the existence of at least one positive solution to the problem under consideration is proven using Krasnosel'skii's theorem on the contraction of a cone in semi-ordered spaces. The uniqueness of such a solution is established by topological methods.
Key words:boundary value problem, positive solution, Green's function, cone compression.
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