Asymptotic Behavior of Even-Order Damped Differential Equations with p-Laplacian like Operators and Deviating Arguments

We study the asymptotic properties of the solutions of a class of even-order damped differential equations with p-Laplacian like operators, delayed and advanced arguments. We present new theorems that improve and complement related contributions reported in the literature. Several examples are provided to illustrate the practicability, maneuverability, and efficiency of the results obtained. An open problem is proposed

First detection of transverse vertical oscillation during the expansion of coronal loops

In this Letter, we perform a detailed analysis of the M5.5-class eruptive flare occurring in active region 12929 on 2022 January 20. The eruption of a hot channel generates a fast coronal mass ejection (CME) and a dome-shaped extreme-ultraviolet (EUV) wave at speeds of 740$-$860 km s$^{-1}$. The CME is associated with a type II radio burst, implying that the EUV wave is a fast-mode shock wave. During the impulsive phase, the flare shows quasi-periodic pulsations (QPPs) in EUV, hard X-ray, and radio wavelengths. The periods of QPPs range from 18 s to 113 s, indicating that flare energy is released and nonthermal electrons are accelerated intermittently with multiple time scales. The interaction between the EUV wave and low-lying adjacent coronal loops (ACLs) results in contraction, expansion, and transverse vertical oscillation of ACLs. The speed of contraction in 171, 193, and 211 {\AA} is higher than that in 304 {\AA}. The periods of oscillation are 253 s and 275 s in 304 {\AA} and 171 {\AA}, respectively. A new scenario is proposed to explain the interaction. The equation that interprets the contraction and oscillation of the overlying coronal loops above a flare core can also interpret the expansion and oscillation of ACLs, suggesting that the two phenomena are the same in essence.Comment: 11 pages, 12 figures, accepted for publication in ApJ