4 citations · 8 across the 7 of their papers we have counts for
7 papers
On ground states for the 2D Schrodinger equation with combined nonlinearities and harmonic potential
Rémi Carles, Yavdat Ilyasov
We consider the nonlinear Schr{ö}dinger equation with a harmonic potential in the presence of two combined energy-subcritical power nonlinearities. We assume that the larger power…
On an optimal potential of Schrödinger operator with prescribed eigenvalue
Yavdat Ilyasov, Nurmukhamet Valeev
The purpose of this paper is twofold: firstly, we present a new type of relationship between inverse problems and nonlinear differential equations. Secondly, we introduce a new typ…
On partially free boundary solutions for elliptic problems with non-Lipschitz nonlinearities
Vladimir Bobkov, Pavel Drábek, Yavdat Ilyasov
We show that the elliptic equation with a non-Lipschitz right-hand side, with and , considered on a smooth star-shaped domain su…
On an inverse spectral problem and a generalized Sturm's nodal theorem for nonlinear boundary value problems
Y. Sh. Ilyasov, N. F. Valeev
We consider an inverse optimization spectral problem for the Sturm-Liouville operator subject to the separated boundary conditions. In the main res…
On the exact multiplicity of stable ground states of non-Lipschitz semilinear elliptic equations for some classes of starshaped sets
J. I. Díaz, J. Hernández, Y. Sh. Ilyasov
We prove the exact multiplicity of flat and compact support stable solutions of an autonomous non-Lipschitz semilinear elliptic equation of eigenvalue type according to the dimensi…
On nonlinear boundary value problem corresponding to -dimensional inverse spectral problem
Y. Sh. Ilyasov, N. F. Valeev
We establish a relationship between an inverse optimization spectral problem for N-dimensional Schrödinger equation and a solution of the nonlinear boundary value prob…
On full Zakharov equation and its approximations
Vladimir Bobkov, Pavel Drábek, Yavdat Ilyasov
We study the solvability of the Zakharov equation in a bounded domain under homogeneous Dirichlet…