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Differentiability of solutions of boundary value problems with respect to data. (English) Zbl 1003.34016
The author proves that the dependence of solutions to the boundary value problem (BVP) \[ X'= f(t,X),\;L(X)= r,\quad\text{where }L: (C^0[a,b], \mathbb{R}^N)\to \mathbb{R}^N, \] on the boundary conditions is continuously differentiable.
Some results on the existence and uniqueness of solutions to nonlinear BVPs, where properties of the variational equations are involved, are established. Particularly, strongly nonlinear BVPs and those multipoint BVPs which admit a point, where all the derivative upto a fixed order \(p\) are given, are dealt with.

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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