5 papers · 1 filter
Cone Minimax Principles for Non-Selfadjoint Operator Pencils
Yavdat Il'yasov, Nur Valeev
We propose a variational approach to principal spectral values of non-selfadjoint operator pencils , where the weight operator may be singu…
Uniqueness of Ground State Solutions for a Defocusing Hartree Equation via Inverse Optimal Problems
Yavdat Il'yasov, Juntao Sun, Nur Valeev +1
We study a generalized defocusing Hartree equation with nonlocal exchange potential and repulsive Hartree--Fock interaction. Using an inverse optimal problem (IOP) approach, we pro…
On finding bifurcations for non-variational elliptic systems by the extended quotients method
Yavdat Il'yasov
We develop a novel method for finding bifurcations for nonlinear systems of equations based on directly finding bifurcations through saddle points of extended quotients. The method…
Existence and uniqueness of a saddle-node bifurcation point for nonlinear equations in general domains
Yavdat Il'yasov
This paper provides a direct method of establishing the existence and uniqueness of saddle-node bifurcations for nonlinear equations in general domains. The method employs the scal…
A new proof of the Perron-Frobeniuos theorem, a variational approach
Yavdat Il'yasov, Nurmukhamet Valeev
We develop the Perron-Frobenius theory using a variational approach and extend it to a set of arbitrary matrices, including those that are neither irreducible nor essentially posit…