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摘要
In this paper, we investigate the following critical elliptic equation -Delta u + V (y) u = u N+2/N-2, u > 0, in R-N, u is an element of H-1 (R-N), where V (y) is a bounded non-negative function in R-N. Assuming that V (y) = V (vertical bar(y) over cap vertical bar, y*), y ((y) over cap = y*) is an element of R-4 x RN-4 and gluing together bubbles with different concentration rates, we obtain new solutions provided that N >= 7, whose concentrating points are close to the point (r(0), y(0)*) which is a stable critical point of the function r(2) V(r, y*) satisfying r(0) > 0 and V(r(0), y(0)*) > 0. In order to construct such new bubble solutions for the above problem, we first prove a non-degenerate result for the positive multi-bubbling solutions constructed in Peng et al. (J Funct Anal 274:2606-2633, 2018) by some local Pohozaev identities, which is of great interest independently. Moreover, we give an example which satisfies the assumptions we impose.
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