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Some boundary value problems for first order scalar functional differential equations. (English) Zbl 1048.34004
Folia Facultatis Scientiarum Naturalium Universitatis Masarykianae Brunensis. Mathematica 10. Brno: Masaryk University (ISBN 80-210-3012-7/pbk). 299 p. (2002).
In Chapter I of the monograph, the boundary value problem $\begin{gathered} u'(t)= l(u)(t)+ q(t),\tag{1}\\ \lambda u(a)+\mu u(b)= c,\tag{2}\end{gathered}$ is considered, where $$l: C([a, b];\mathbb{R})\to L([a, b];\mathbb{R})$$ is a linear bounded operator, $$q\in L([a, b];\mathbb{R})$$, $$\lambda,\mu,c\in\mathbb{R}$$ and $$|\lambda|+ |\mu|\neq 0$$, while, in Chapter 11, the nonlinear boundary value problem $\begin{gathered} u'(t)= F(u)(t),\tag{3}\\ \lambda u(a)+\mu u(b)= h(u),\tag{4}\end{gathered}$ is studied, where $$F: C([a, b];\mathbb{R})\to L([a, b];\mathbb{R})$$, $$h:C([a, b]:\mathbb{R})\to \mathbb{R}$$ are continuous operators satisfying the Carathéodory conditions and $$\lambda$$, $$\mu\in\mathbb{R}$$, $$|\lambda|+ |\mu|\neq 0$$.
Sufficient conditions for existence and uniqueness of solutions of problems (1)–(2) and (3)–(4) are proved.

##### MSC:
 34-02 Research exposition (monographs, survey articles) pertaining to ordinary differential equations 34K10 Boundary value problems for functional-differential equations