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On a weighted boundary value problem for a system of singular functional-differential equations. (English) Zbl 0984.34057

A system of functional-differential equations \[ u''(t)= f(u)(t) \tag{1} \] with the boundary conditions \[ \lim_{t\to a}u(t)= 0,\quad \lim_{t\to b} u(t)=0, \tag{2} \]
\[ \sup\biggl\{(t -\alpha)^{\alpha-1} (b-t)^{\beta-1}\bigl \|u(t)\bigr\|+ (t-a)^\alpha (b-t)^\beta\bigl \|u'(t)\bigr \|:a<t< b \biggr\}< +\infty, \] is considered, with \(0\leq\alpha\), \(\beta\leq 1\). Sufficient conditions for the solvability of problem (1)–(2) are established.

MSC:

34K10 Boundary value problems for functional-differential equations
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