Alexander Lomtatidze, Department of Mathematical Analysis, Faculty of Science, Masaryk University, Janackovo nam. 2a, 662 95 Brno, CZECH REPUBLIC
Jiri Sremr, Department of Mathematical Analysis, Faculty of Science, Masaryk University, Janackovo nam. 2a, 662 95 Brno, CZECH REPUBLIC
E-mail: hakl@ipm.cz, bacho@math.muni.cz, sremr@math.muni.cz
Abstract. Nonimprovable, in a certain sense, sufficient conditions for the unique solvability of the boundary value problem $$ u'(t)=\ell(u)(t)+q(t),\qquad u(a)+\lambda u(b)=c $$ are established, where $\ell: C([a,b];R)\to L([a,b]; R)$ is a linear bounded operator, $q\in L([a,b];R)$, $\lambda\in R_+$, and $c\in R$. The question on the dimension of the solution space of the homogeneous problem $$ u'(t)=\ell(u)(t),\qquad u(a)+\lambda u(b)=0 $$ is discussed as well.
AMSclassification. 34K06, 34K10.
Keywords. Linear functional differential equation, antiperiodic type BVP, solvability and unique solvability.