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Keywords:
second-order $p$-Laplacian Hamiltonian systems; impulsive effect; critical point theory
second-order $p$-Laplacian Hamiltonian systems; impulsive effect; critical point theory
Summary:
The purpose of this paper is to study the existence and multiplicity of a periodic solution for the non-autonomous second-order system \begin {gather} \frac {{\rm d}}{{\rm d}t}(|\dot {u}(t)|^{p-2}\dot {u}(t)) =\nabla F(t, u(t)),\quad \text {\rm a.e.}\ t\in [0,T],\nonumber \\ u(0)-u(T)=\dot {u}(0)-\dot {u}(T)=0,\nonumber \\ \Delta \dot {u}^i(t_{j})=\dot {u}^i(t_j^+)-\dot {u}^i(t_j^-)=I_{ij}(u^i(t_j)),\ i = 1, 2,\dots , N;\ j = 1, 2,\dots ,m.\nonumber \end {gather} By using the least action principle and the saddle point theorem, some new existence theorems are obtained for second-order $p$-Laplacian systems with or without impulse under weak sublinear growth conditions, improving some existing results in the literature.
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