On the existence of multiple periodic solutions for the vector $p$-Laplacian via critical point theory

Lü, Haishen, O'Regan, Donal, and Agarwal, Ravi P.. "On the existence of multiple periodic solutions for the vector $p$-Laplacian via critical point theory." Applications of Mathematics 50.6 (2005): 555-568. <http://eudml.org/doc/33238>.

@article{Lü2005,
abstract = {We study the vector $p$-Laplacian \[ \left\rbrace \begin\{array\}\{ll\}-(| u^\{\prime \}| ^\{p-2\}u^\{\prime \})^\{\prime \}=\nabla F(t,u) \quad \text\{a.e.\}\hspace\{5.0pt\}t\in [0,T], u(0) =u(T),\quad u^\{\prime \}(0)=u^\{\prime \}(T),\quad 1<p<\infty . \end\{array\}\right. \qquad \mathrm \{(*)\}\] 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.},
author = {Lü, Haishen, O'Regan, Donal, Agarwal, Ravi P.},
journal = {Applications of Mathematics},
keywords = {$p$-Laplacian equation; periodic solution; critical point theory; -Laplacian equation; periodic solution; critical point theory},
language = {eng},
number = {6},
pages = {555-568},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the existence of multiple periodic solutions for the vector $p$-Laplacian via critical point theory},
url = {http://eudml.org/doc/33238},
volume = {50},
year = {2005},
}

TY - JOUR
AU - Lü, Haishen
AU - O'Regan, Donal
AU - Agarwal, Ravi P.
TI - On the existence of multiple periodic solutions for the vector $p$-Laplacian via critical point theory
JO - Applications of Mathematics
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 6
SP - 555
EP - 568
AB - We study the vector $p$-Laplacian \[ \left\rbrace \begin{array}{ll}-(| u^{\prime }| ^{p-2}u^{\prime })^{\prime }=\nabla F(t,u) \quad \text{a.e.}\hspace{5.0pt}t\in [0,T], u(0) =u(T),\quad u^{\prime }(0)=u^{\prime }(T),\quad 1<p<\infty . \end{array}\right. \qquad \mathrm {(*)}\] 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.
LA - eng
KW - $p$-Laplacian equation; periodic solution; critical point theory; -Laplacian equation; periodic solution; critical point theory
UR - http://eudml.org/doc/33238
ER -