9 citations · 19 across the 8 of their papers we have counts for
8 papers
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…
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…
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…
Rayleigh quotients of the level set manifolds related to the nonlinear PDE
Yavdat Il'yasov
The main topic of this note is a discussion of applicability conditions of the Nehari manifold method depending on the value of parameters of equations. As the main tool, we apply…
Flat solutions of some non-Lipschitz autonomous semilinear equations may be stable for
Jesús Ildefonso Díaz, Jesús Hernández, Yavdat Il'yasov
We prove that flat ground state solutions ( minimizing the energy and with gradient vanishing on the boundary of the domain) of the Dirichlet problem associated to some semil…
On critical exponents curve for nonlinear elliptic equations in zero mass case
Yavdat Il'yasov
Semilinear elliptic equations of the form in bounded and unbounded domains are considered. In the plane of exponents , the so-called criti…
Maximal existence domains of positive solutions for two-parametric systems of elliptic equations
Vladimir Bobkov, Yavdat Il'yasov
The paper is devoted to the study of two-parametric families of Dirichlet problems for systems of equations with -Laplacians and indefinite nonlinearities. Continuous and mon…
Hopf maximum principle violation for elliptic equations with non-Lipschitz nonlinearity
Yavdat Il'yasov, Youri Egorov
We consider elliptic equations with non-Lipschitz nonlinearity in a smooth bounded domain , , with Dirichlet bound…