A nonexistence result for sign-changing solutions of the Brezis-Nirenberg problem in low dimensions

作者：Iacopetti Alessandro^*; Pacella Filomena

来源：Journal of Differential Equations, 2015, 258(12): 4180-4208.

DOI：10.1016/j.jde.2015.01.030

• Semilinear elliptic equations
• Critical exponent
• Sign-changing solutions
• Asymptotic behavior

We consider the Brezis-Nirenberg problem:
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where Omega is a smooth bounded domain in R-N, N >= 3,2* = 2N/N-2 is the critical Sobolev exponent and lambda > 0 is a positive parameter.
The main result of the paper shows that if N = 4, 5, 6 and lambda is close to zero, there are no sign-changing solutions of the form
u(lambda) = PU delta 1,xi, PU delta 2,xi,+ omega(lambda),
where PU delta is the projection on H-0(1)(Omega) of the regular positive solution of the critical problem in RN, centered at a point xi epsilon Omega and w(lambda) is a remainder term.
Some additional results on norm estimates of w(lambda), and about the concentrations speeds of tower of bubbles in higher dimensions are also presented.

• 出版日期2015-6-15