Mieko Tanaka

activity

20142025

(p, q)

-Laplace equations with two parameters

37 citations · 97 across the 10 of their papers we have counts for

collaborators

10 papers

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.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.AP2022★ 3 cited

On the antimaximum principle for the $p$ -Laplacian and its sublinear perturbations

Vladimir Bobkov, Mieko Tanaka

We investigate qualitative properties of weak solutions of the Dirichlet problem for the equation $- Δ_{p} u = λm (x) ∣ u ∣^{p - 2} u + η a (x) ∣ u ∣^{q - 2} u + f (x)$ in a bounded domain $Ω\subset…

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★ 2 cited

Multiplicity of positive solutions for $(p, q)$ -Laplace equations with two parameters

Vladimir Bobkov, Mieko Tanaka

We study the zero Dirichlet problem for the equation $- Δ_{p} u - Δ_{q} u = α ∣ u ∣^{p - 2} u + β ∣ u ∣^{q - 2} u$ in a bounded domain $Ω \subset R^{N}$ , with $1 < q < p$ . We investigate the relatio…

math.AP2020★ 15 cited

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.AP2018★ 4 cited

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.AP2017★ 17 cited

Remarks on minimizers for $(p, q)$ -Laplace equations with two parameters

Vladimir Bobkov, Mieko Tanaka

We study in detail the existence, nonexistence and behavior of global minimizers, ground states and corresponding energy levels of the $(p, q)$ -Laplace equation $-Δ_p u -Δ_q u = α|u…

math.AP2016★ 15 cited

On sign-changing solutions for $(p, q)$ -Laplace equations with two parameters

Vladimir Bobkov, Mieko Tanaka

We investigate the existence of nodal (sign-changing) solutions to the Dirichlet problem for two-parametric family of partially homogeneous $(p, q)$ -Laplace equations $-Δ_p u -Δ_q u…

math.AP2014★ 37 cited

On positive solutions for $(p, q)$ -Laplace equations with two parameters

Vladimir Bobkov, Mieko Tanaka

We study the existence and non-existence of positive solutions for the $(p, q)$ -Laplace equation $- Δ_{p} u - Δ_{q} u = α ∣ u ∣^{p - 2} u + β ∣ u ∣^{q - 2} u$ , where $p \neq = q$ , under the zero Diri…

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

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

On the antimaximum principle for the p-Laplacian and its sublinear perturbations

On subhomogeneous indefinite p-Laplace equations in supercritical spectral interval

Multiplicity of positive solutions for (p,q)-Laplace equations with two parameters

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

Remarks on minimizers for (p,q)-Laplace equations with two parameters

On sign-changing solutions for (p,q)-Laplace equations with two parameters

On positive solutions for (p,q)-Laplace equations with two parameters

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

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

On the antimaximum principle for the $p$ -Laplacian and its sublinear perturbations

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

Multiplicity of positive solutions for $(p, q)$ -Laplace equations with two parameters

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

Remarks on minimizers for $(p, q)$ -Laplace equations with two parameters

On sign-changing solutions for $(p, q)$ -Laplace equations with two parameters

On positive solutions for $(p, q)$ -Laplace equations with two parameters