Blowing up of sign-changing solutions to a subcritical problem

Bouh, Kamal Ould

doi:10.1007/s00229-014-0700-z

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“…It is easy to see that a necessary condition for solving the problem is that K has to be positive somewhere. Note that some related problems of type (P ε ), in case of bounded domains, were studied in [4,5,9,[12][13][14] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Construction of sign-changing solutions for a harmonic equation with subcritical exponent

Bouh

2015

Monatsh Math

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In this paper, we study the harmonic equation involving subcritical exponentunit ball in R n , n ≥ 5 with Euclidean metric g 0 , ∂B n = S n−1 is its boundary, K is a function on S n−1 and ε is a small positive parameter. We construct solutions of the subcritical equation (P ε ) which blow up at two different critical points of K . Furthermore, we construct solutions of (P ε ) which have two bubbles and blow up at the same critical point of K .

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Section: Introductionmentioning

confidence: 99%