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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
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