On unbounded solutions of the first order ordinary differential equations

Abstract

The article is concerned with Cauchy problem
G_x(x, ξ) + H (x, G(x, ξ)) = 0,
G(ξ, ξ)= + ∞
Let H(x, y), H_y(x,y) ∈ C(R²) and
H(x, y) ≻ a₁ |y|^1+a +a₂
where a₁, a₂ ≻ 0. Then there exists the unique solution G(x, ξ) of Cauchy problem and it is general solution of this equation.