Abstract
Let n≥2 denote an integer, and let l∈{1,…,n−1}. A family of (l+1)-point boundary value problems for an n-th order ordinary differential equation is studied and sufficient conditions for existence of solutions are obtained. In particular, it is shown that a type of global uniqueness of solutions implies global existence of solutions. Then explicit conditions in terms of monotonicity of the nonlinear term are obtained to imply the global uniqueness of solutions.
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