Infinitely many solutions for higher order impulsive equations without symmetry (Q2080693)

The authors consider a class of boundary value problems with impulses at fixed times \begin{align*} &\sum_{i=0}^m (-1)^{m-i} A_iu^{(2m-2i)}(t) = |u(t)|^{q-2}u(t) + g(t,u(t)), \quad t \ne t_k, \,t\in (0,T), \\ &\triangle u^{(m-1+j)}(t_k) = I_{jk}(u^{(m-j)}(t_k)), \quad j = 1,\ldots,m, \ k = 1,\ldots,p,\\ &u(0) = u'(0) = \ldots = u^{(m-1)}(0) = 0, \ u(T) = u'(T) = \ldots = u^{(m-1)}(T) = 0, \end{align*} where \(0 < t_1 < \ldots < t_p < T\), \(A_i \in {\mathbb R}\), \(q > 2\), \(p,m\) are positive integers, \(I_{jk}\), \(g\) are continuous. Sufficient conditions ensuring the existence of infinitely many solutions are given. The approach is based on variational and perturbative methods.