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![https://www.impan.pl/download/pdf/ap100-1-8 [zdalny]](images/mime-icons/pdf.gif "ap100-1-8.pdf")
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Abstrakty
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
⎩ $Δu'(t_{j}) = u'(t⁺_{j} - u'(t¯_{j}) = I_{j}(u(t_{j}))$, 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.
⎧ u''(t) + g(t)u'(t) + f(t,u(t)) = 0, a.e. t ∈ [0,T
⎨ u(0) = u(T) = 0
⎩ $Δu'(t_{j}) = u'(t⁺_{j} - u'(t¯_{j}) = I_{j}(u(t_{j}))$, 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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
87-98
Opis fizyczny
Daty
wydano
2011
Twórcy
autor
- Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, People's Republic of China
autor
- Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, People's Republic of China
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-ap100-1-8
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