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 / Pistoia, Angela; Vaira, Giusi. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - STAMPA. - 119(2014), pp. 330-340. [10.1016/j.na.2014.10.023]
From periodic ODE's to supercritical PDE's
PISTOIA, Angela;VAIRA, GIUSI
2014
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 allegati a questo prodotto
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