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Keywords:
generic properties; periodic boundary value problem
generic properties; periodic boundary value problem
Summary:
It is shown that for a given system of linearly independent linear continuous functionals $l_i C^{n-1} \to\bb R$, $i=1,\dots,n$, the set of all $n$-th order linear differential equations such that the Green function for the corresponding generalized boundary value problem (BVP for short) exists is open and dense in the space of all $n$-th order linear differential equations. Then the generic properties of the set of all solutions to nonlinear BVP-s are investigated in the case when the nonlinearity in the differential equation has a linear majorant. A periodic BVP is also studied.
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