Nondegeneracy

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Ray Yang - One of the best experts on this subject based on the ideXlab platform.

Changlin Xiang - One of the best experts on this subject based on the ideXlab platform.

Denis Bonheure - One of the best experts on this subject based on the ideXlab platform.

Guoyuan Chen - One of the best experts on this subject based on the ideXlab platform.

Juncheng Wei - One of the best experts on this subject based on the ideXlab platform.

  • Nondegeneracy of nodal solutions to the critical yamabe problem
    Communications in Mathematical Physics, 2015
    Co-Authors: Monica Musso, Juncheng Wei
    Abstract:

    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 $$-\Delta Q= |Q|^{\frac{2}{n-2}} Q, \quad Q \in {\mathcal D}^{1,2}(\mathbb{R}^n).$$ 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.

  • Nondegeneracy of nonradial nodal solutions to yamabe problem
    arXiv: Analysis of PDEs, 2014
    Co-Authors: Monica Musso, Juncheng Wei
    Abstract:

    We provide the first example of a sequence of {\em nondegenerate}, in the sense of Duyckaerts-Kenig-Merle \cite{DKM}, nodal nonradial solutions to the critical Yamabe problem $$ -\Delta Q= |Q|^{\frac{2}{n-2}} Q, \ \ Q \in {\mathcal D}^{1,2} (\R^n). $$