Resonant singular boundary value problems (Q1915733)

Under some conditions the problem (1) \({1 \over p(t) q(t)} (p(t) y')' + \lambda_0 \) \(y = f(t,y,p (t)y')\) a.e. on \([0,1]\), (2) \(\lim_{t \to 0 +} p(t) y'(t) = 0\), \(ay (1) + b \lim_{t \to 1 -} p (t) y'(t) = 0\), \(a > 0\), \(b \geq 0\) has a solution \(y \in C[0,1] \cap C^1 (0,1)\) with \(py' \in AC [0,1] \). \(\lambda_0\) is the first eigenvalue of \(- {1 \over p(t) q(t)} (p(t)y')' = \lambda y\), (2).