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Existence of solutions for two-point boundary value problems. (English) Zbl 0797.34019
The author considers different types of inhomogeneous boundary conditions (Dirichlet, Neumann, mixed) for the scalar second order ordinary differential equation \(x''= f(t,x,x')\), \(0\leq t\leq 1\), where \(f\) is continuous. The main results are proved using the topological transversality theorems due to Granas. Sufficient conditions on \(f\), that insure a priori bounds on solutions, are provided. Several examples are also discussed.

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
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