Resumen de New Results for Some Damped Dirichlet Problems with Impulses

Huiwen Chen, Zhimin He, Zigen Ouyang, Maoxin Liao

• 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 ].