Given a 3-dimensional Riemannian manifold (M, g), we investigate the existence of positive solutions of the Klein-Gordon-Maxwell system [GRAPHICS] and Schrodinger-Maxwell system [GRAPHICS] when p is an element of (2, 6). We prove that if epsilon is small enough, any stable critical point xi(0) of the scalar curvature of g generates a positive solution (u(epsilon), v(epsilon)) to both the systems such that u(epsilon) concentrates at xi(0) as epsilon goes to zero.
THE ROLE OF THE SCALAR CURVATURE IN SOME SINGULARLY PERTURBED COUPLED ELLIPTIC SYSTEMS ON RIEMANNIAN MANIFOLDS / Marco, Ghimenti; Anna Maria, Micheletti; Pistoia, Angela. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 34:6(2014), pp. 2535-2560. [10.3934/dcds.2014.34.2535]
THE ROLE OF THE SCALAR CURVATURE IN SOME SINGULARLY PERTURBED COUPLED ELLIPTIC SYSTEMS ON RIEMANNIAN MANIFOLDS
PISTOIA, Angela
2014
Abstract
Given a 3-dimensional Riemannian manifold (M, g), we investigate the existence of positive solutions of the Klein-Gordon-Maxwell system [GRAPHICS] and Schrodinger-Maxwell system [GRAPHICS] when p is an element of (2, 6). We prove that if epsilon is small enough, any stable critical point xi(0) of the scalar curvature of g generates a positive solution (u(epsilon), v(epsilon)) to both the systems such that u(epsilon) concentrates at xi(0) as epsilon goes to zero.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
