Volume 47, Issue 4
Infinitely Many Clark Type Solutions to a p(x)-Laplace Equation

J. Math. Study, 47 (2014), pp. 379-387.

Published online: 2014-12

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• Abstract

In this paper, the following p(x)-Laplacian equation: $Δ_{p(x)}u+V(x)|u|^{p(x)-2}u=Q(x) f (x,u)$, $x∈R^N$, is studied. By applying an extension of Clark's theorem, the existence of infinitely many solutions as well as the structure of the set of critical points near the origin are obtained.

• Keywords

Clark theorem infinitely many solutions p(x)-Laplace variational methods

35A15, 35A05, 35J70

zhouzhengslx@163.com (Zheng Zhou)

xsi@xmut.edu.cn (Xin Si)

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@Article{JMS-47-379, author = {Zhou , Zheng and Si , Xin}, title = {Infinitely Many Clark Type Solutions to a p(x)-Laplace Equation}, journal = {Journal of Mathematical Study}, year = {2014}, volume = {47}, number = {4}, pages = {379--387}, abstract = {

In this paper, the following p(x)-Laplacian equation: $Δ_{p(x)}u+V(x)|u|^{p(x)-2}u=Q(x) f (x,u)$, $x∈R^N$, is studied. By applying an extension of Clark's theorem, the existence of infinitely many solutions as well as the structure of the set of critical points near the origin are obtained.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v47n4.14.02}, url = {http://global-sci.org/intro/article_detail/jms/9963.html} }
TY - JOUR T1 - Infinitely Many Clark Type Solutions to a p(x)-Laplace Equation AU - Zhou , Zheng AU - Si , Xin JO - Journal of Mathematical Study VL - 4 SP - 379 EP - 387 PY - 2014 DA - 2014/12 SN - 47 DO - http://doi.org/10.4208/jms.v47n4.14.02 UR - https://global-sci.org/intro/article_detail/jms/9963.html KW - Clark theorem KW - infinitely many solutions KW - p(x)-Laplace KW - variational methods AB -

In this paper, the following p(x)-Laplacian equation: $Δ_{p(x)}u+V(x)|u|^{p(x)-2}u=Q(x) f (x,u)$, $x∈R^N$, is studied. By applying an extension of Clark's theorem, the existence of infinitely many solutions as well as the structure of the set of critical points near the origin are obtained.

Zheng Zhou & Xin Si. (2020). Infinitely Many Clark Type Solutions to a p(x)-Laplace Equation. Journal of Mathematical Study. 47 (4). 379-387. doi:10.4208/jms.v47n4.14.02
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