V. Bobkov

activity

20142026

(p, q)

-Laplace equations with two parameters

37 citations · 203 across the 35 of their papers we have counts for

collaborators

36 papers

math.AP2026

Remarks on the antimaximum principle

Vladimir Bobkov

We present several observations on the antimaximum principle (AMP) for the model problem $- Δ_{p} u = λ ∣ u ∣^{p - 2} u + f$ in a bounded smooth domain $Ω$ , subject to the zero Dirichlet b…

math.AP2025

On Rayleigh quotients connected to $p$ -Laplace equations with polynomial nonlinearities

Vladimir Bobkov, Mieko Tanaka

Let $Ω$ be a bounded open set and $p, q, r > 1$ . The main observation of the present work is the following: $W_{0}^{1, p} (Ω)$ -solutions of the equation $- Δ_{p} u = μ ∣ u ∣^{q - 2} u + ∣ u ∣^{r - 2} u$ …

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.AP2023★ 1 cited

Reverse Faber-Krahn and Szego-Weinberger type inequalities for annular domains under Robin-Neumann boundary conditions

T. V. Anoop, Vladimir Bobkov, Pavel Drabek

Let $τ_{k} (Ω)$ be the $k$ -th eigenvalue of the Laplace operator in a bounded domain $Ω$ of the form $Ω_{out} ∖ B_{α}$ under the Neumann boundary condition on…

math.AP2023★ 4 cited

Abstract multiplicity results for $(p, q)$ -Laplace equations with two parameters

Vladimir Bobkov, Mieko Tanaka

We investigate the existence and multiplicity of abstract weak solutions of the equation $- Δ_{p} u - Δ_{q} u = α ∣ u ∣^{p - 2} u + β ∣ u ∣^{q - 2} u$ in a bounded domain under zero Dirichlet boundary…

math.AP2023★ 1 cited

Nonuniqueness for fractional parabolic equations with sublinear power-type nonlinearity

Jiří Benedikt, Vladimir Bobkov, Raj Narayan Dhara +1

We show that the parabolic equation $u_{t} + (- Δ)^{s} u = q (x) ∣ u ∣^{α - 1} u$ posed in a time-space cylinder $(0, T) \times R^{N}$ and coupled with zero initial condition and zero…

Remarks on the antimaximum principle

On Rayleigh quotients connected to p-Laplace equations with polynomial nonlinearities

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

Reverse Faber-Krahn and Szego-Weinberger type inequalities for annular domains under Robin-Neumann boundary conditions

Abstract multiplicity results for (p,q)-Laplace equations with two parameters

Nonuniqueness for fractional parabolic equations with sublinear power-type nonlinearity

On Rayleigh quotients connected to $p$ -Laplace equations with polynomial nonlinearities

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

Abstract multiplicity results for $(p, q)$ -Laplace equations with two parameters