2 citations · 2 across the 3 of their papers we have counts for
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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 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…
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…