V. Bobkov

activity

20182026

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Showing 2018Show all

6 papers · 1 filter

math.AP2018

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, $- Δ u = λ ∣ u ∣^{β - 1} u - ∣ u ∣^{α - 1} u$ with $λ > 0$ and $0 < α < β < 1$ , considered on a smooth star-shaped domain $Ω$ su…

math.AP2018

On the Fredholm-type theorems and sign properties of solutions for $(p, q)$ -Laplace equations with two parameters

Vladimir Bobkov, Mieko Tanaka

We consider the Dirichlet problem for the nonhomogeneous equation $- Δ_{p} u - Δ_{q} u = α ∣ u ∣^{p - 2} u + β ∣ u ∣^{q - 2} u + f (x)$ in a bounded domain, where $p \neq = q$ , and $α, β \in R$ …

math.AP2018

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 $- Δ_{p} u = λ ∣ u ∣^{p - 2} u + f (x)$ with positive $f \in L^{\infty} (Ω)$ states the existence of a critical value $λ_f >…

math.AP2018

On maximum and comparison principles for parabolic problems with the $p$ -Laplacian

Vladimir Bobkov, Peter Takac

We investigate strong and weak versions of maximum and comparison principles for a class of quasilinear parabolic equations with the $p$ -Laplacian $$ \partial_t u - Δ_p u = λ|u|^{p…

math.CA2018

Asymptotic relation for zeros of cross-product of Bessel functions and applications

Vladimir Bobkov

Let $a_{ν, k}$ be the $k$ -th positive zero of the cross-product of Bessel functions $J_{ν} (R z) Y_{ν} (z) - J_{ν} (z) Y_{ν} (R z)$ , where $ν \geq 0$ and $R > 1$ . We derive an initial value proble…

math.AP2018

On exact Pleijel's constant for some domains

Vladimir Bobkov

We provide an explicit expression for the Pleijel constant for the planar disk and some of its sectors, as well as for $N$ -dimensional rectangles. In particular, the Pleijel consta…

On partially free boundary solutions for elliptic problems with non-Lipschitz nonlinearities

On the Fredholm-type theorems and sign properties of solutions for (p,q)-Laplace equations with two parameters

Estimates on the spectral interval of validity of the anti-maximum principle

On maximum and comparison principles for parabolic problems with the p-Laplacian

Asymptotic relation for zeros of cross-product of Bessel functions and applications

On exact Pleijel's constant for some domains

On the Fredholm-type theorems and sign properties of solutions for $(p, q)$ -Laplace equations with two parameters

On maximum and comparison principles for parabolic problems with the $p$ -Laplacian