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2013 INFINITELY MANY HOMOCLINIC ORBITS OF SECOND-ORDER $p$-LAPLACIAN SYSTEMS
Xiaoyan Lin, Xianhua Tang
Taiwanese J. Math. 17(4): 1371-1393 (2013). DOI: 10.11650/tjm.17.2013.2518

Abstract

In this paper, we give several new sufficient conditions for the existence of infinitely many homoclinic orbits of the second-order ordinary $p$-Laplacian system $$ \frac{d}{dt} \left(|\dot{u}(t)|^{p-2} \dot{u}(t)\right) - a(t) |u(t)|^{p-2} u(t) + \nabla W(t,u(t)) = 0, $$ where $p \gt 1, \ t\in {\mathbb{R}},\ u\in {\mathbb{R}}^{N}$, $a\in C({\mathbb{R}}, {\mathbb{R}})$ and $W\in C^{1}({\mathbb{R}}\times {\mathbb{R}}^{N}, {\mathbb{R}})$ are no periodic in $t$, which greatly improve the known results due to Rabinowitz and Willem.

Citation

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Xiaoyan Lin. Xianhua Tang. "INFINITELY MANY HOMOCLINIC ORBITS OF SECOND-ORDER $p$-LAPLACIAN SYSTEMS." Taiwanese J. Math. 17 (4) 1371 - 1393, 2013. https://doi.org/10.11650/tjm.17.2013.2518

Information

Published: 2013
First available in Project Euclid: 10 July 2017

zbMATH: 1293.34060
MathSciNet: MR3085516
Digital Object Identifier: 10.11650/tjm.17.2013.2518

Subjects:
Primary: 34C37, 58E05, 70H05

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

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Vol.17 • No. 4 • 2013
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