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 (vertical bar y((n-1))vertical bar(lambda-1)y((n-1)))' = alpha 0p(t)e(sigma y), where alpha(0) epsilon {-1, 1}, sigma, lambda epsilon R \ {0}, and p : [a,w[->]0, +infinity[ (-infinity < a < w <= + infinity) is a continuously differentiable function. We also establish asymptotic representations of such solutions.