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

• Autorzy: Jianwen Zhou , Yongkun Li
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 49J35: Minimax problems
• 34B37: Boundary value problems with impulses

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2011
• Tom: 100
• Numer: 1
• Strony: 87-98

Daty

wydano

2011

Twórcy

autor

Jianwen Zhou

• Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, People's Republic of China

autor

Yongkun Li

• Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, People's Republic of China

Identyfikatory

DOI

10.4064/ap100-1-8