We study the fractional Laplacian system with critical exponent
where is a smooth bounded domain, , stands for the fractional Laplacian, is the critical Sobolev exponent, , and , here is the first eigenvalue of with Dirichlet boundary condition. For each fixed , we show that this system has a positive least energy solution.
Submitted September 25, 2015. Published June 20, 2016.
Math Subject Classifications: 35R11, 35J50, 35B33.
Key Words: Positive least energy solution; critical exponent; fractional Laplacian system.
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| Qingfang Wang |
School of Mathematics and Computer Science
Wuhan Polytechnic University
Wuhan 430023, China
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