Multiplicity results for superlinear boundary value problems with impulsive effects (Q2800517)

The authors treat the nonlinear Dirichlet boundary value problem with impulses at fixed times: NEWLINE\[NEWLINE \begin{aligned} &-(p(t)u'(t))' + q(t) u(t) = \lambda f(t,u(t)), \;t \in [0,T],\;t \neq t_j,\\ &u(0) = u(T) = 0,\\ &u'(t_j^+) - u'(t_j^-) = \mu I_j(u(t_j)), \;j = 1,2,\ldots,n, \end{aligned} NEWLINE\]NEWLINE where \(p \in C^1([0,T];(0,\infty))\), \(q \in L^\infty([0,T])\), \(\lambda, \mu > 0\), \(f : [0,T]\times \mathbb{R} \to \mathbb{R}\), \(0 < t_1 < \ldots < t_n < T\), \(I_j : \mathbb{R} \to \mathbb{R}\) are continuous.NEWLINENEWLINESufficient conditions for the existence of at least one (Theorem 3.1) and two (Theorem 3.2) nontrivial solutions to the boundary value problem are obtained. To this goal the critical point theory is used.