On the solutions of a singular elliptic equation concentrating on two orthogonal spheres
Manna, B. B. · Srikanth, P. N.
Original · EN
Let A={x∈ ²ᵐ: 0< a< |x| <b} be an annulus. Consider the following singularly perturbed elliptic problem on A equation arraylll -² u + |x|ηu = |x|ηuᵖ, & in A u>0 & in A u = 0 & on ∂ A array %a1 equation 1<p<2*-1. We shall prove the existence of a positive solution u which concentrates on two different orthogonal spheres of dimension (m-1) as → 0. We achieve this by studying a reduced problem on an annular domain in ᵐ⁺¹ and analyzing the profile of a two point concentrating solution in this domain.
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