V. Bobkov

activity

20182021

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8 papers · 1 filter

math.AP2021

On subhomogeneous indefinite $p$ -Laplace equations in supercritical spectral interval

Vladimir Bobkov, Mieko Tanaka

We study the existence, multiplicity, and certain qualitative properties of solutions to the zero Dirichlet problem for the equation $- Δ_{p} u = λ ∣ u ∣^{p - 2} u + a (x) ∣ u ∣^{q - 2} u$ in a bo…

math.AP2020

Generalized Picone inequalities and their applications to $(p, q)$ -Laplace equations

Vladimir Bobkov, Mieko Tanaka

We obtain a generalization of the Picone inequality which, in combination with the classical Picone inequality, appears to be useful for problems with the $(p, q)$ -Laplace type oper…

math.AP2020

Existence and multiplicity results for a class of semilinear elliptic equations

Vladimir Bobkov, Pavel Drabek, Jesus Hernandez

We study the existence and multiplicity of nonnegative solutions, as well as the behaviour of corresponding parameter-dependent branches, to the equation $- Δ u = (1 - u) u^{m} - λ u^{n}$ i…

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 >…

On subhomogeneous indefinite p-Laplace equations in supercritical spectral interval

Generalized Picone inequalities and their applications to (p,q)-Laplace equations

Existence and multiplicity results for a class of semilinear elliptic equations

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 subhomogeneous indefinite $p$ -Laplace equations in supercritical spectral interval

Generalized Picone inequalities and their applications to $(p, q)$ -Laplace equations

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