Asymptotic representations of solutions of two-term nonautonomous nth-order ordinary differential equations with exponential nonlinearity

We obtain necessary and sufficient conditions for the existence of a certain class of solutions of the differential equation $$ (|y^{(n - 1)} |^{\lambda - 1} y^{(n - 1)} )' = \alpha _0 p(t)e^{\sigma y} $$ , where α ₀ ∈ {?1, 1}, σ, λ ∈ R \ {0}, and p: a, ω→]0,+∞(?∞ < a < ω ≤ + ∞) is a continuously differentiable function. We also establish asymptotic representations of such solutions.