30 citations · 36 across the 11 of their papers we have counts for
12 papers
On the Minimax Bifurcation Formula
Y. Sh. Il'yasov
We introduce a Rayleigh-quotient minimax method for locating maximal one-sided saddle-node bifurcations in nonlinear equations, including non-variational ones. The method avoids br…
On the asymptotics of ground states for a boundary value problem for the equation
Yavdat Sh. Il'yasov, Elvira I. Turianova
We study a singularly perturbed Dirichlet problem for the -Laplacian with competing superlinear terms, \[ -\varepsilon Δ_p u = a(x)|u|^{q-2}u - b(x)|u|^{γ-2}u, \qquad u|_{\parti…
On prescribed energy saddle-point solutions to indefinite problems
Yavdat Il'yasov, Edcarlos D. Silva, Maxwell L. Silva
A minimax variational principle for saddle-point solutions with prescribed energy levels is introduced. The approach is based on the development of the linking theorem to the energ…
On periodic and compactly supported least energy solutions to semilinear elliptic equations with non-Lipschitz nonlinearity
Jacques Giacomoni, Yavdat Il'yasov, Deepak Kumar
We discuss the existence and non-existence of periodic in one variable and compactly supported in the other variables least energy solutions for equations with non-Lipschitz nonlin…
Existence of S-shaped type bifurcation curve with dual cusp catastrophe via variational methods
Marcos Leandro Carvalho, Yavdat Il'yasov, Carlos Alberto Santos
We discuss the existence of multiple positive solutions leading to the occurrence of an S-shaped bifurcation curve to the equations of the form $$ -Δ_p u= f(μ,λ, u)~ \mbox{in} ~Ω\s…
On orbital stability of the physical ground states of the NLS equations
Yavdat Il'yasov
We prove orbital stability result for physical ground states of a nonlinear Schrödinger (NLS) equation in the sense that the set of these ground states is contained in the set of p…
On a generalized Collatz-Wielandt formula and finding saddle-node bifurcations
Yavdat Il'yasov
We introduce the nonlinear generalized Collatz-Wielandt formula and prove that its s…
Separating of critical points on the Nehari manifold via the nonlinear generalized Rayleigh quotients
Marcos L. M. Carvalho, Yavdat Sh. Il'yasov, Carlos Alberto Santos
In this paper, we deal with equations of variational form which Nahari manifolds can contain more than two different types of critical points. We introduce a method of separating c…
Estimates on the spectral interval of validity of the anti-maximum principle
Vladimir Bobkov, Pavel Drabek, Yavdat Il'yasov
The anti-maximum principle for the homogeneous Dirichlet problem to with positive states the existence of a critical value $λ_f >…
On branches of positive solutions for p-Laplacian problems at the extreme value of Nehari manifold method
Yavdat Il'yasov, Kaye Silva
This paper is concerned with variational continuation of branches of solutions for nonlinear boundary value problems, which involve the p-Laplacian, the indefinite nonlinearity, an…
On extreme values of Nehari manifold method via nonlinear Rayleigh's quotient
Yavdat Il'yasov
We study applicability conditions of the Nehari manifold method for the equation of the form in a Banach space , where is a real parameter. Our stud…
Computation of maximal turning points by a variational approach
Yavdat Il'yasov, Alexsandr Ivanov
We develop a new paradigm for finding bifurcations of solutions of nonlinear problems, which is based on the detection of extreme values of new type of variational functional assoc…