S. Kolonitskii

activity

20122024

most citedOn a property of the nodal set of least energy sign-changing solutions for quasilinear elliptic equations

5 citations · 14 across the 7 of their papers we have counts for

collaborators

7 papers

math.AP2024

Payne nodal set conjecture for the fractional $p$ -Laplacian in Steiner symmetric domains

Vladimir Bobkov, Sergey Kolonitskii

Let $u$ be either a second eigenfunction of the fractional $p$ -Laplacian or a least energy nodal solution of the equation $(- Δ)_{p}^{s} u = f (u)$ with superhomogeneous and subcritic…

math.AP2024

Entire solutions to the Swift--Hohenberg equation via variational approach

S. B. Kolonitskii, L. M. Lerman, A. I. Nazarov

We study the stationary Swift--Hohenberg equation $(Δ + 1)^{2} u - α u - β u^{2} + u^{3} = 0$ in the whole space $R^{n}$ , $2 \leq n \leq 7$ . We develop and modify the variational approach…

math.AP2022★ 3 cited

Improved Friedrichs inequality for a subhomogeneous embedding

Vladimir Bobkov, Sergey Kolonitskii

For a smooth bounded domain $Ω$ and $p \geq q \geq 2$ , we establish quantified versions of the classical Friedrichs inequality $∥\nabla u ∥_{p}^{p} - λ_{1} ∥ u ∥_{q}^{p} \geq 0$ , $u \in W_0…

math.AP2018

Second-order derivative of domain-dependent functionals along Nehari manifold trajectories

Vladimir Bobkov, Sergey Kolonitskii

Assume that a family of domain-dependent functionals $E_{Ω_{t}}$ possesses a corresponding family of least energy critical points $u_{t}$ which can be found as (possibly nonunique) min…

math.AP2017★ 5 cited

On a property of the nodal set of least energy sign-changing solutions for quasilinear elliptic equations

Vladimir Bobkov, Sergei Kolonitskii

In this note we prove the Payne-type conjecture about the behaviour of the nodal set of least energy sign-changing solutions for the equation $- Δ_{p} u = f (u)$ in bounded Steiner sym…

math.AP2017★ 3 cited

On qualitative properties of solutions for elliptic problems with the $p$ -Laplacian through domain perturbations

Vladimir Bobkov, Sergey Kolonitskii

We study the dependence of least nontrivial critical levels of the energy functional corresponding to the zero Dirichlet problem $- Δ_{p} u = f (u)$ in a bounded domain $Ω\subset \math…

math.AP2012★ 3 cited

Multiplicity of 1D-concentrating positive solutions to the Dirichlet problem for equation with $p$ -Laplacian

Sergey B. Kolonitskii

We prove the multiplicity of spike-layer type solutions to the Dirichlet problem for the equation $- Δ_{p} u = u^{q - 1}$ in expanding annuli.

Payne nodal set conjecture for the fractional p-Laplacian in Steiner symmetric domains

Entire solutions to the Swift--Hohenberg equation via variational approach

Improved Friedrichs inequality for a subhomogeneous embedding

Second-order derivative of domain-dependent functionals along Nehari manifold trajectories

On a property of the nodal set of least energy sign-changing solutions for quasilinear elliptic equations

On qualitative properties of solutions for elliptic problems with the p-Laplacian through domain perturbations

Multiplicity of 1D-concentrating positive solutions to the Dirichlet problem for equation with p-Laplacian

Payne nodal set conjecture for the fractional $p$ -Laplacian in Steiner symmetric domains

On qualitative properties of solutions for elliptic problems with the $p$ -Laplacian through domain perturbations

Multiplicity of 1D-concentrating positive solutions to the Dirichlet problem for equation with $p$ -Laplacian