Nondegeneracy of Nonradial Nodal Solutions to Yamabe Problem
نویسندگان
چکیده
We prove the existence of a sequence of nondegenerate, in the sense of Duyckaerts-Kenig-Merle [9], nodal nonradial solutions to the critical Yamabe problem −∆Q = |Q| 2 n−2Q, Q ∈ D1,2(Rn). This is the first example in the literature of nondegeneracy for nodal nonradial solutions of nonlinear elliptic equations and it is also the only nontrivial example for which the result of Duyckaerts-Kenig-Merle [9] applies.
منابع مشابه
Desingularization of Clifford Torus and Nonradial Solutions to Yamabe Problem with Maximal Rank
Through desingularization of Clifford torus, we prove the existence of a sequence of nondegenerate (in the sense of Duyckaerts-Kenig-Merle ([?])) nodal nonradial solutions to the critical Yamabe problem −∆u = n(n− 2) 4 |u| 4 n−2 u, u ∈ D(R). The case n = 4 is the first example in the literature of a solution with maximal rank N = 2n+ 1 + n(n−1) 2 . Introduction Consider the problem −∆u = γ|u|p−...
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Let (M, g) be a compact Riemannian manifold of dimension n ≥ 3. We define the second Yamabe invariant as the infimum of the second eigenvalue of the Yamabe operator over the metrics conformal to g and of volume 1. We study when it is attained. As an application, we find nodal solutions of the Yamabe equation.
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