Let (M,g) be an n-dimensional compact Riemannian manifold without boundary and Γ be a non-degenerate closed geodesic of (M,g). We prove that the supercritical problem. -δ<inf>g</inf>u+hu=un+1n-3±ε,u>0, in (M,g) has a solution that concentrates along Γ as ε goes to zero, provided the function h and the sectional curvatures along Γ satisfy a suitable condition. A connection with the solution of a class of periodic Ordinary Differential Equations with singularity of attractive or repulsive type is established.

Bubbling solutions for supercritical problems on manifolds

VAIRA, Giusi
2015

Abstract

Let (M,g) be an n-dimensional compact Riemannian manifold without boundary and Γ be a non-degenerate closed geodesic of (M,g). We prove that the supercritical problem. -δgu+hu=un+1n-3±ε,u>0, in (M,g) has a solution that concentrates along Γ as ε goes to zero, provided the function h and the sectional curvatures along Γ satisfy a suitable condition. A connection with the solution of a class of periodic Ordinary Differential Equations with singularity of attractive or repulsive type is established.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11591/368444
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