Existence of solutions for a class of damped vibration problems on time scales.
Some sufficient conditions on the existence and multiplicity of solutions for the damped vibration problems with impulsive effects ⎧ u”(t) + g(t)u’(t) + f(t,u(t)) = 0, a.e. t ∈ [0,T ⎨ u(0) = u(T) = 0 ⎩ , j = 1,...,p, are established, where , g ∈ L¹(0,T;ℝ), f: [0,T] × ℝ → ℝ is continuous, and , j = 1,...,p, are continuous. The solutions are sought by means of the Lax-Milgram theorem and some critical point theorems. Finally, two examples are presented to illustrate the effectiveness of our results....
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