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On positive stable solutions to weighted quasilinear problems with negative exponent

Authors: 

Phuong Le, Huy Thao Nguyen & Thi Yen Nguyen

Source title: 
Complex Variables and Elliptic Equations, 2017 (ISI)
Academic year of acceptance: 
2018-2019
Abstract: 

https://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/gcov20/0/gcov20.ahead-of-print/17476933.2017.1403429/20171127/images/gcov_a_1403429_um0001.gifLet https://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/gcov20/0/gcov20.ahead-of-print/17476933.2017.1403429/20171127/images/gcov_a_1403429_ilm0001.gif and https://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/gcov20/0/gcov20.ahead-of-print/17476933.2017.1403429/20171127/images/gcov_a_1403429_ilm0002.gif, we prove the nonexistence of positive stable https://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/gcov20/0/gcov20.ahead-of-print/17476933.2017.1403429/20171127/images/gcov_a_1403429_ilm0003.gif solutions of weighted quasilinear problem

 

 

The result holds true for  https://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/gcov20/0/gcov20.ahead-of-print/17476933.2017.1403429/20171127/images/gcov_a_1403429_ilm0004.gif    or  https://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/gcov20/0/gcov20.ahead-of-print/17476933.2017.1403429/20171127/images/gcov_a_1403429_ilm0005.gif and https://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/gcov20/0/gcov20.ahead-of-print/17476933.2017.1403429/20171127/images/gcov_a_1403429_ilm0006.gif, which is a positive critical exponent. Here https://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/gcov20/0/gcov20.ahead-of-print/17476933.2017.1403429/20171127/images/gcov_a_1403429_ilm0007.gif and https://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/gcov20/0/gcov20.ahead-of-print/17476933.2017.1403429/20171127/images/gcov_a_1403429_ilm0008.gif are nonnegative functions such that https://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/gcov20/0/gcov20.ahead-of-print/17476933.2017.1403429/20171127/images/gcov_a_1403429_ilm0009.gif and https://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/gcov20/0/gcov20.ahead-of-print/17476933.2017.1403429/20171127/images/gcov_a_1403429_ilm0010.gif for large |x|. We also construct an example to show the sharpness of our result.