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Abstract
We study the existence of sign changing solutions to the following problem {Δu+u^{p−1}u=0inΩ_{ε};u=0on∂Ω_{ε}, where [Formula presented] is the critical Sobolev exponent and Ω_{ε} is a bounded smooth domain in R^{n}, n≥3, of the form Ω_{ε}=Ω\B(0,ε). Here Ω is a smooth bounded domain containing the origin 0 and B(0,ε) denotes the ball centered at the origin with radius ε>0. We construct a new type of signchanging solutions with high energy to problem (0.1), when the parameter ε is small enough.
Original language  English 

Pages (fromto)  916962 
Number of pages  47 
Journal  Journal of Differential Equations 
Volume  271 
Early online date  24 Sept 2020 
DOIs  
Publication status  Published  15 Jan 2021 
Keywords
 Concentration phenomenon of solutions
 Coron's problem
 Critical Sobolev exponent
 Signchanging solutions
ASJC Scopus subject areas
 Analysis
 Applied Mathematics
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Concentration phenomena in nonlinear analysis
Engineering and Physical Sciences Research Council
27/04/20 → 31/03/24
Project: Research council