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Multiple positive solutions of Dirichlet boundary value problems for second order impulsive differential equations. (English) Zbl 1103.34015
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 $t=t_{k}.$

34B37Boundary value problems for ODE with impulses
34B18Positive solutions of nonlinear boundary value problems for ODE
Full Text: DOI
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