On a weighted boundary value problem for a system of singular functional-differential equations (Q2712567)

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