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