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On the Existence of Multiple Periodic Solutions for the Vector <Emphasis Type="Italic">p</Emphasis>-Laplacian via Critical Point Theory

Authors:

Haishen Lu Donal O'Regan Ravi P Agarwal

Institution:

(1) Department of Applied Mathematics, Hohai University, Nanjing, 210098, China;(2) Department of Mathematics, National University of Ireland, Galway, Ireland;(3) Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, Florida, 32901, USA

Abstract:

We study the vector p-Laplacian

$(*)\quad \quad \quad \quad \quad \quad \quad \left\{ {_{u(0) = u(T),\quad u'(0) = u'(T),\quad 1 < p < \infty .}^{ - (|u'|^{p - 2} u')' = \nabla F(t,u)\quad \operatorname{a} .e.\quad t \in 0,T],} } \right.$

We prove that there exists a sequence (u _n) of solutions of (*) such that u _n is a critical point of ϕ and another sequence (u _n ^* ) of solutions of (*) such that u _n ^* is a local minimum point of ϕ, where ϕ is a functional defined below. The research is supported by NNSF of China (10301033).

Keywords:

p-Laplacian equation periodic solution critical point theory

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