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Volume 32, Issue 2
Existence of Solutions to Elliptic Equation with Exponential Nonlinearities and Singular Term

Yimin Xue & Shouting Chen

J. Part. Diff. Eq., 32 (2019), pp. 156-170.

Published online: 2019-07

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  • Abstract

In this paper, we consider an elliptic equation with exponential nonlinearities and singular term. By constructing the corresponding variational framework, and using a Singular Trudinger-Moser inequality due to Li, Mountain-pass theorem and the Ekeland’s variational principle, we get a nontrivial positive weak solution.

  • Keywords

Singular Trudinger-Moser inequality Mountain-pass theorem exponential growth.

  • AMS Subject Headings

35J60, 46E35

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xueym@xzit.edu.cn (Yimin Xue)

stchen1980@163.com (Shouting Chen)

  • BibTex
  • RIS
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@Article{JPDE-32-156, author = {Yimin and Xue and xueym@xzit.edu.cn and 4333 and School of Mathematics and Physics, Xuzhou University of Technology, Xuzhou 221018, China and Yimin Xue and Shouting and Chen and stchen1980@163.com and 4991 and School of Mathematics and Physics, Xuzhou University of Technology, Xuzhou 221018, China and Shouting Chen}, title = {Existence of Solutions to Elliptic Equation with Exponential Nonlinearities and Singular Term}, journal = {Journal of Partial Differential Equations}, year = {2019}, volume = {32}, number = {2}, pages = {156--170}, abstract = {

In this paper, we consider an elliptic equation with exponential nonlinearities and singular term. By constructing the corresponding variational framework, and using a Singular Trudinger-Moser inequality due to Li, Mountain-pass theorem and the Ekeland’s variational principle, we get a nontrivial positive weak solution.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v32.n2.5}, url = {http://global-sci.org/intro/article_detail/jpde/13240.html} }
TY - JOUR T1 - Existence of Solutions to Elliptic Equation with Exponential Nonlinearities and Singular Term AU - Xue , Yimin AU - Chen , Shouting JO - Journal of Partial Differential Equations VL - 2 SP - 156 EP - 170 PY - 2019 DA - 2019/07 SN - 32 DO - http://doi.org/10.4208/jpde.v32.n2.5 UR - https://global-sci.org/intro/article_detail/jpde/13240.html KW - Singular Trudinger-Moser inequality KW - Mountain-pass theorem KW - exponential growth. AB -

In this paper, we consider an elliptic equation with exponential nonlinearities and singular term. By constructing the corresponding variational framework, and using a Singular Trudinger-Moser inequality due to Li, Mountain-pass theorem and the Ekeland’s variational principle, we get a nontrivial positive weak solution.

Yimin Xue & Shouting Chen . (2019). Existence of Solutions to Elliptic Equation with Exponential Nonlinearities and Singular Term. Journal of Partial Differential Equations. 32 (2). 156-170. doi:10.4208/jpde.v32.n2.5
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