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An application of variational methods to Dirichlet boundary value problem with impulses. (English) Zbl 1191.34039

The authors consider the impulsive Dirichlet boundary value problem

-u '' (t)+λu(t)=f(t,u(t))+p(t),t[0,T],u ' (t j )=I j (u(t j )),j=1,,k,u(0)=u(T)=0,

where 0<t 1 <<t k <T are impulse instants, the impulsive functions I j : and the right-hand side f are continuous, pL 2 [0,T], λ>-π 2 /T 2 . Sufficient conditions for the existence of at least one and infinitely many weak solutions are found. The proofs are based on the critical points theory.

MSC:
34B37Boundary value problems for ODE with impulses
58E05Abstract critical point theory
47J30Variational methods (nonlinear operator equations)
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