Singlepoint condensation and leastenergy solutions
Authors:
Xiaofeng Ren and Juncheng Wei
Journal:
Proc. Amer. Math. Soc. 124 (1996), 111120
MSC (1991):
Primary 35B40, 35A08, 35A15; Secondary 34A34
MathSciNet review:
1301045
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Abstract: We prove a conjecture raised in our earlier paper which says that the leastenergy solutions to a twodimensional semilinear problem exhibit singlepoint condensation phenomena as the nonlinear exponent gets large. Our method is based on a sharp form of a wellknown borderline case of the Sobolev embedding theory. With the help of this embedding, we can use the Moser iteration scheme to carefully estimate the upper bound of the solutions. We can also determine the location of the condensation points.
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Additional Information
Xiaofeng Ren
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Address at time of publication:
Institute for Mathematics & Applications, University of Minnesota, Minneapolis, Minnesota 55455
Email:
ren@ima.umn.edu
Juncheng Wei
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Address at time of publication:
Department of Mathematics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong
DOI:
http://dx.doi.org/10.1090/S0002993996031565
PII:
S 00029939(96)031565
Received by editor(s):
July 2, 1994
Communicated by:
Jeffrey Rauch
Article copyright:
© Copyright 1996
American Mathematical Society
