Existence and Uniqueness of Homoclinic Solution for a Rayleigh Equation with a Singularity

• Lu, Shiping ^[1] ; Jia Xuewen ^[1]
  1. [1] Nanjing University of Information Science and Technology

     Nanjing University of Information Science and Technology

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 1, 2020
• Idioma: inglés
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• Resumen

  • The problem of homoclinic solutions is considered for a singular Rayleigh equation x′′(t)+f(x′(t))-g(x(t))-α(t)x(t)1-x(t)=h(t),where f,g,h,α:R→R are continuous and α(t) is T-periodic. By using a continuation theorem of coincidence degree principle, some new results on the existence and uniqueness of homoclinic solution to the equation are obtained.