Existence and multiplicity of solutions for a class of damped vibration problems with impulsive effects

Jianwen Zhou, and Yongkun Li. "Existence and multiplicity of solutions for a class of damped vibration problems with impulsive effects." Annales Polonici Mathematici 100.1 (2011): 87-98. <http://eudml.org/doc/286119>.

@article{JianwenZhou2011,
abstract = {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 ⎩ $Δu^\{\prime \}(t_\{j\}) = u^\{\prime \}(t⁺_\{j\} - u^\{\prime \}(t¯_\{j\}) = I_\{j\}(u(t_\{j\}))$, j = 1,...,p, are established, where $t₀ = 0 < t₁ < ⋯ < t_\{p\} < t_\{p+1\} = T$, g ∈ L¹(0,T;ℝ), f: [0,T] × ℝ → ℝ is continuous, and $I_\{j\}: ℝ → ℝ$, 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.},
author = {Jianwen Zhou, Yongkun Li},
journal = {Annales Polonici Mathematici},
language = {eng},
number = {1},
pages = {87-98},
title = {Existence and multiplicity of solutions for a class of damped vibration problems with impulsive effects},
url = {http://eudml.org/doc/286119},
volume = {100},
year = {2011},
}

TY - JOUR
AU - Jianwen Zhou
AU - Yongkun Li
TI - Existence and multiplicity of solutions for a class of damped vibration problems with impulsive effects
JO - Annales Polonici Mathematici
PY - 2011
VL - 100
IS - 1
SP - 87
EP - 98
AB - 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 ⎩ $Δu^{\prime }(t_{j}) = u^{\prime }(t⁺_{j} - u^{\prime }(t¯_{j}) = I_{j}(u(t_{j}))$, j = 1,...,p, are established, where $t₀ = 0 < t₁ < ⋯ < t_{p} < t_{p+1} = T$, g ∈ L¹(0,T;ℝ), f: [0,T] × ℝ → ℝ is continuous, and $I_{j}: ℝ → ℝ$, 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.
LA - eng
UR - http://eudml.org/doc/286119
ER -