A multiplicity result for second order impulsive differential equations via the Leggett Williams fixed point theorem
The authors consider the following boundary value problem for an impulsive differential equation of second order \[ \begin{gathered} y''(t)+ \varphi(t)f(y(t))= 0,\quad t\in (0,1)\setminus\{t_1,\dots, t_m\},\quad 0< t_1<\cdots< t_m< 1,\\ \Delta y(t_k)= I_k(y(t^-_k)),\quad k= 1,\dots, m,\\ \Delta y'(t_k)= J_k(y'(t^-_k)),\quad k=1,\dots, m,\\ y(0)= y(1)= 0.\end{gathered}\tag{1} \] By means of the Leggett-Williams fixed-point theorem, the existence of three nonnegative solutions of (1) is proved.
second-order impulse differential equations
scientific article; zbMATH DE number 2136196