On unbounded solutions of the first order ordinary differential equations

Abstract

The article is concerned with Cauchy problem Gx(x, ξ) + H (x, G(x, ξ)) = 0, G(ξ, ξ)= + ∞ Let H(x, y), Hy(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.