We investigate the Henon type equation involving the critical Sobolev exponent with Dirichret boundary condition
in included in a unit ball, under several conditions. Here, is a non-trivial given function with which may vanish on . Let be the first eigenvalue of the Dirichret eigenvalue problem in . We show that if the dimension and , there exists a positive solution for small . Our methods include the mountain pass theorem and the Talenti function.
Submitted April 2, 2018. Published November 28, 2018.
Math Subject Classifications: 35J20, 35J60, 35J61, 35J91.
Key Words: Critical Sobolev exponent; Henon equation; mountain pass theorem; Talenti function.
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| Kazune Takahashi |
Graduate School of Mathematical Sciences
The University of Tokyo
3-8-1 Komaba Meguroku Tokyo 153-8914, Japan
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