ORIGINAL ARTICLE
Single-peak solution for a fractional slightly subcritical problem with non-power nonlinearity
Shengbing Deng,
Fang Yu,
Corresponding Author
Shengbing Deng
School of Mathematics and Statistics, Southwest University, Chongqing, People's Republic of China
Correspondence
Shengbing Deng, School of Mathematics and Statistics, Southwest University, Chongqing 400715, People's Republic of China.
Email: [email protected]
Search for more papers by this authorFang Yu
School of Mathematics and Statistics, Southwest University, Chongqing, People's Republic of China
Search for more papers by this authorShengbing Deng,
Fang Yu,
Corresponding Author
Shengbing Deng
School of Mathematics and Statistics, Southwest University, Chongqing, People's Republic of China
Correspondence
Shengbing Deng, School of Mathematics and Statistics, Southwest University, Chongqing 400715, People's Republic of China.
Email: [email protected]
Search for more papers by this authorFang Yu
School of Mathematics and Statistics, Southwest University, Chongqing, People's Republic of China
Search for more papers by this authorFirst published: 30 June 2024
Abstract
We consider the following fractional problem involving slightly subcritical non-power nonlinearity,
where is a smooth bounded domain in , , , is the fractional critical Sobolev exponent and is a small parameter, is the spectral fractional Laplacian operator. We construct a positive bubbling solution, which concentrates at a nondegenerate critical point of the Robin function by Lyapunov–Schmidt reduction procedure.
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