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Interior bubbling solutions for the crit...
del Pino, Manuel...
Interior bubbling solutions for the critical Lin-Ni-Takagi problem in dimension 3 by del Pino, Manuel ( Author )
N.A
10-12-2015
We consider the problem of finding positive solutions of the problem Δu−λu+u5=0 in a bounded, smooth domain Ω in R3, under zero Neumann boundary conditions. Here λ is a positive number. We analyze the role of Green's function of −Δ+λ in the presence of solutions exhibiting single bubbling behavior at one point of the domain when λ is regarded as a parameter. As a special case of our results, we find and characterize a positive value λ∗ such that if λ−λ∗>0 is sufficiently small, then this problem is solvable by a solution uλ which blows-up by bubbling at a certain interior point of Ω as λ↓λ∗.
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Article
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36.88 KB
English
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MYR 0.01
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https://arxiv.org/abs/1512.03468
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