Resumen de Periodic solutions for a class of asymptotically linear damped vibration problems with resonance at infinity

Yuanhao Wang, Zihan Zhang, Guanggang Liu

• In this paper, we consider a class of asymptotically linear damped vibration problems with resonance at infinity. Compared with the existing results, under this resonance condition the functional corresponding to the problem may not satisfy the compactness condition. By combining the penalized functional technique, Morse theory and two critical point theorems, we obtain the existence and multiplicity of nontrivial periodic solutions.