R. Hakl, A. Lomtatidze, and J. \v Sremr

On constant sign solutions of a periodic type boundary value problems for first order functional differential equations

In this paper the question on the existence and uniqueness of a constant sign solution of a periodic type boundary value problem is studied. More precisely, the nonimprovable effective sufficient conditions for a linear bounded operator $\ell:\cabr\to\labr$ are established guaranteeing that the problem $$ u'(t)=\ell(u)(t)+q(t),\qquad u(a)-\lambda u(b)=c, $$ where $q\in\labrp$, $\lambda$ $\in\rp$, has a unique solution, and this solution does not change its sign.

Mathematics Subject Classification: 34K06, 34K10.

Key words and phrases: Linear functional differential equation, periodic type boundary value problem, solvability and unique solvability.