Geodesic
On the existence of multiple periodic solutions for the vector $p$-Laplacian via critical point theory
Applications of Mathematics, Tome 50 (2005) no. 6, pp. 555-568.

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We study the vector $p$-Laplacian \[ \left\rbrace \begin{array}{ll}-(| u^{\prime }| ^{p-2}u^{\prime })^{\prime }=\nabla F(t,u) \quad \text{a.e.}\hspace{5.0pt}t\in [0,T], u(0) =u(T),\quad u^{\prime }(0)=u^{\prime }(T),\quad 1\infty . \end{array}\right. \qquad \mathrm{(*)}\] We prove that there exists a sequence $(u_n)$ of solutions of ($*$) such that $u_n$ is a critical point of $\varphi $ and another sequence $(u_n^{*}) $ of solutions of $(*)$ such that $u_n^{*}$ is a local minimum point of $\varphi $, where $\varphi $ is a functional defined below.
DOI : 10.1007/s10492-005-0037-8
Classification : 34B15, 34C25
Keywords: $p$-Laplacian equation; periodic solution; critical point theory 
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Lü, Haishen; O'Regan, Donal; Agarwal, Ravi P. On the existence of multiple periodic solutions for the vector $p$-Laplacian via critical point theory. Applications of Mathematics, Tome 50 (2005) no. 6, pp. 555-568. doi : 10.1007/s10492-005-0037-8. http://geodesic.mathdoc.fr/articles/10.1007/s10492-005-0037-8/

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