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Variational method to the impulsive equation with Neumann boundary conditions. (English) Zbl 1184.34039

The authors consider the impulsive boundary value problem

-(p(t)u ' (t)) ' +r(t)u ' (t)+q(t)u(t)=g(t,u(t)),a.e.t[0,1],tt k ,-(p(t k )u ' (t k ))=I k (u(t k )),k=1,...,p-1,u ' (0+)=u ' (1-)=0,

where 0<t 1 <...<t p-1 <1; pC 1 ([0,1]), r, qC([0,1]), g, I k are continuous functions. Sufficient conditions for the existence of at least one (two, infinitely many) solutions are obtained by using a variational approach and critical point theorems.

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