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In this note we prove in the nonlinear setting of $CD(K,\infty)$ spaces thestability of the Krasnoselskii spectrum of the Laplace operator $-\Delta$ undermeasured Gromov-Hausdorff convergence, under an additional compactnessassumption satisfied, for instance, by sequences of $CD^*(K,N)$ metric measurespaces with uniformly bounded diameter. Additionally, we show that everyelement $\lambda$ in the Krasnoselskii spectrum is indeed an eigenvalue, namelythere exists a nontrivial $u$ satisfying the eigenvalue equation $- \Delta u =\lambda u$.

Continuity of nonlinear eigenvalues in $CD(K,\infty)$ spaces with respect to measured Gromov-Hausdorff convergence