Interior bubbling solutions for the critical Lin-Ni-Takagi problem in dimension 3
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Date
2019
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Abstract
We consider the problem of finding positive solutions of the problem u -.u + u5 = 0 in a bounded, smooth domain in R3, under zero Neumann boundary conditions. Here. is a positive number. We analyze the role of Green's function of - +. in the presence of solutions exhibiting single bubbling behavior at one point of the domain when. is regarded as a parameter. As a special case of our results, we find and characterize a positive value.* such that if. -. * > 0 is sufficiently small, then this problem is solvable by a solution u. which blows-up by bubbling at a certain interior point of lambda down arrow lambda(*).