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Zbl 1103.34015
Lin, Xiaoning; Jiang, Daqing
Multiple positive solutions of Dirichlet boundary value problems for second order impulsive differential equations.
(English)
[J] J. Math. Anal. Appl. 321, No. 2, 501-514 (2006). ISSN 0022-247X

By using the theory of fixed-point index in cones, the authors prove the existence of multiple positive solutions for the Dirichlet boundary value problem with impulse effect $$-x''=f(t,x), \quad t\ne t_{k}, \quad k=1,2,\ldots,m, \ t\in J:=[0,1],$$ $$x'(t_{k}^{-})-x'(t_{k}^{+})=I_{k}(x(t_{k})),$$ $$x(0)=x(1)=0,$$ where $f\in C(J\times {\Bbb R}^{+},{\Bbb R}^{+}),$ $I_{k}\in C({\Bbb R}^{+},{\Bbb R}^{+}),$ $0<t_1<t_2<\ldots<t_m<1$ and $x'(t_{k}^{+}), x'(t_{k}^{-})$ denote the right and left limits of $x'(t)$ at $t=t_{k}.$
[Sotiris K. Ntouyas (Ioannina)]
MSC 2000:
*34B37 Boundary value problems with impulses
34B18 Positive solutions of nonlinear boundary value problems

Keywords: Dirichlet boundary value problem with impulse effect; multiple positive solutions; fixed-point index

Cited in: Zbl 1208.34032

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