Solution of a certain singular Cauchy problem (Q1901957)

The author considers the singular Cauchy problem (1) \(\alpha (t)(x')^n = a_1t + a_2x + f(t,x,x')\), \(x(0) = 0\), where \(n\) is a positive integer, \(a_i \neq 0\) are constants, \(\alpha : (0, \tau] \to (0,+ \infty)\) is a continuously differentiable function with \(\lim_{t \to + 0} \alpha (t) = 0\). In two theorems he presents sufficient conditions for (1) to have a continuum of solutions or to have a unique solution.