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math.AP2026
Compactly Supported Solutions near a Nehari Critical Value
J. I. Dıaz, J. Hernandez, Y. Ilyasov
We study non-negative solutions of the indefinite sublinear Dirichlet problem $$ \left \{\ \begin{array}{ll} -Δu=λu+m(x)|u|^{α-1}u&\quad\hbox{ in },\\ u=0&\quad \hbox{ on $\part…
math.AP2026
Exact Rayleigh Reduction for Direct Detection of Turning Bifurcations
Yavdat Il'yasov
We introduce an exact Rayleigh reduction for the direct construction and detection of turning bifurcations in nonlinear parameter-dependent equations. A generalized Rayleigh functi…
cs.LG2026
Cone Rayleigh Levels: Finite Perturbations and Certified Control
Yavdat Sh. Il'yasov, Nur F. Valeev
We study the reuse of positive trial profiles under finite perturbations of nonsymmetric matrix pencils B-λG. The lower and upper cone Rayleigh levels need not coincide and are def…