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A multiplicity result for second order impulsive differential equations via the Leggett Williams fixed point theorem. (English) Zbl 1070.34042
The authors consider the following boundary value problem for an impulsive differential equation of second order $$\gathered y''(t)+ \varphi(t)f(y(t))= 0,\quad t\in (0,1)\setminus\{t_1,\dots, t_m\},\quad 0< t_1<\cdots< t_m< 1,\\ \Delta y(t_k)= I_k(y(t^-_k)),\quad k= 1,\dots, m,\\ \Delta y'(t_k)= J_k(y'(t^-_k)),\quad k=1,\dots, m,\\ y(0)= y(1)= 0.\endgathered\tag1$$ By means of the Leggett-Williams fixed-point theorem, the existence of three nonnegative solutions of (1) is proved.

34B37Boundary value problems for ODE with impulses
34A37Differential equations with impulses
34B18Positive solutions of nonlinear boundary value problems for ODE
Full Text: DOI
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