New Results for Some Damped Dirichlet Problems with Impulses

• Chen, Huiwen ^[1] ; He, Zhimin ^[2] ; Ouyang, Zigen ^[1] ; Liao, Maoxin ^[1]
  1. [1] University of South China

     University of South China

     China

     
  2. [2] Central South University

     Central South University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 2, 2022
• Idioma: inglés
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• Resumen

  • This paper investigate the following damped nonlinear impulsive differential equations.

    −u(t) + p(t)u (t) + q(t)u(t) f (t, u(t)), a.e. t ∈ [0, T ], u (tj) Ij(u(tj)), j 1, 2,..., m, u(0) u(T ) 0.

    Applying fountain theorem and a new analytical approach, we obtain that the aforementioned problem has infinitely many solutions under the local superlinear condition lim|u|→+∞ u 0 f (t,s)ds u2 +∞ uniformly in t ∈ (a,b) for some (a,b) ⊂ [0, T ] instead of the global superlinear condition lim|u|→+∞ u 0 f (t,s)ds u2 +∞ uniformly in t ∈ [0, T ].