New Results for Some Damped Dirichlet Problems with Impulses

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], Δ u'(t_j ) = I_j (u(t_j )),[ 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 | → + ∞∫_0^uf(t,s)ds/u^2 = + ∞ uniformly in t ∈ (a,b) for some (a,b) ⊂ [0,T] instead of the global superlinear condition lim_| u | → + ∞∫_0^uf(t,s)ds/u^2 = + ∞ uniformly in t ∈ [0,T] .