We consider a nonlocal eigenvalue problem which arises in the study of stability of point-condensation solutions in some reaction-diiusion systems. We give some suucient (and explicit) conditions for the stability in the general case.

In this paper, the concepts of Pareto H -eigenvalue and Pareto Z -eigenvalue are introduced for studying constrained minimization problem and the necessary and sufficient conditions of such eigenvalues are given. It is proved that a symmetric tensor has at least one Pareto H -eigenvalue (Pareto Z -eigenvalue). Furthermore, theminimumPareto H -eigenvalue (or Pareto Z -eigenvalue) of a symmetric ...