Abstract Let (M,g) be an m-dimensional compact Riemannian manifold without boundary. Assume κ ∈ C2(M) is such that -Δg+κ is coercive. We prove the existence of solutions to the supercritical problems -Δgu+κu=up,u>0in(M,g)and-Δgu+κu=λeuin(M,g) which concentrate along an (m-1)-dimensional submanifold of M as p→∞ and λ→0, respectively, under suitable symmetry assumptions on the manifold M. A connection with the solutions of a class of periodic ODE's is established.
From periodic ODE's to supercritical PDE's
Vaira G.
2015-01-01
Abstract
Abstract Let (M,g) be an m-dimensional compact Riemannian manifold without boundary. Assume κ ∈ C2(M) is such that -Δg+κ is coercive. We prove the existence of solutions to the supercritical problems -Δgu+κu=up,u>0in(M,g)and-Δgu+κu=λeuin(M,g) which concentrate along an (m-1)-dimensional submanifold of M as p→∞ and λ→0, respectively, under suitable symmetry assumptions on the manifold M. A connection with the solutions of a class of periodic ODE's is established.File in questo prodotto:
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