Given (M,g) the set {(\eps, h) in (0, 1) X S^k : any solution u in A of -\eps^2\Delta_g u + u = u^{p-1}, u > 0 in M is non degenerate} is a residual subset of (0,1) X B_r where \Delta_g is the laplace beltrami operator, \eps is a small real parameter and p > 2 if N = 2 and 2 < p < 2* = 2N/(N-)2 if N>2, B_r is a suitable ball centered at 0 with radius r in the Banach space S^k, S^k is the space of all C^k symmetric covariant 2-tensors on M and A is a bounded subset of H^1_g (M) which does not contain the constant function 1.
Generic properties of singularly perturbed non linear elliptic problems on Riemannian manifolds
MICHELETTI, ANNA MARIA;
2009-01-01
Abstract
Given (M,g) the set {(\eps, h) in (0, 1) X S^k : any solution u in A of -\eps^2\Delta_g u + u = u^{p-1}, u > 0 in M is non degenerate} is a residual subset of (0,1) X B_r where \Delta_g is the laplace beltrami operator, \eps is a small real parameter and p > 2 if N = 2 and 2 < p < 2* = 2N/(N-)2 if N>2, B_r is a suitable ball centered at 0 with radius r in the Banach space S^k, S^k is the space of all C^k symmetric covariant 2-tensors on M and A is a bounded subset of H^1_g (M) which does not contain the constant function 1.File in questo prodotto:
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