Existence of positive solutions for a second order periodic boundary value problem with impulsive effects
Keywords
Periodic boundary value problem, fixed point theorem, positive solution, coneAbstract
In this paper, we are mainly concerned with the existence and multiplicity of positive solutions for the following second order periodic boundary value problem involving impulsive effects $$ \begin{cases} -u''+\rho^2u=f(t,u), & t\in J',\\ -\Delta u'|_{t=t_k}=I_k(u(t_k)), & k=1,\ldots,m,\\ u(0)-u(2\pi)=0,\quad u'(0)-u'(2\pi)=0. \end{cases} $$ Here $J'=J\setminus \{t_1,\ldots, t_m\}$, $f\in C(J\times \mathbb{R}^+, \mathbb{R}^+)$, $I_k\in C( \mathbb{R}^+, \mathbb{R}^+)$, where $ \mathbb{R}^+=[0,\infty)$, $J=[0,2\pi]$. The proof of our main results relies on the fixed point theorem on cones. The paper extends some previous results and reports some new results about impulsive differential equations.Downloads
Published
2016-04-12
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1.
XU, Jiafa, WEI, Zhongli and DING, Youzheng. Existence of positive solutions for a second order periodic boundary value problem with impulsive effects. Topological Methods in Nonlinear Analysis. Online. 12 April 2016. Vol. 43, no. 1, pp. 11 - 22. [Accessed 26 April 2024].
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