Yasuhito Miyamoto

activity

20152026

most citedA limit equation and bifurcation diagrams of semilinear elliptic equations with general supercritical growth

36 citations · 79 across the 21 of their papers we have counts for

collaborators

21 papers

math.AP2026

Monotonicity of the bifurcation curve for supercritical elliptic problems in the borderline dimension $N = 10$

Kenta Kumagai, Yasuhito Miyamoto

We study the global structure of bifurcation diagrams for semilinear elliptic Dirichlet problems with supercritical nonlinearities in the unit ball. In particular, we focus on the…

math.AP2026

Classification of the structures of stable radial solutions for semilinear elliptic equations in $R^{N}$

Yasuhito Miyamoto, Yūki Naito

We study the stability of radial solutions of the semilinear elliptic equation $Δ u + f (u) = 0$ in $R^{N}$ , where $N \geq 3$ and $f$ is a general superciritical nonlinearity. We gi…

math.AP2025

Non-uniqueness of positive solutions for supercritical semilinear heat equations without scale invariance

Kotaro Hisa, Yasuhito Miyamoto

We establish nonuniqueness of solutions for Cauchy problems of semilinear heat equations with a wide class of nonlinearities. Specifically, we consider \[ \begin{cases} \partial_tu…

math.AP2025

The Gierer-Meinhardt system in the entire space with non-local proliferation rates

Marius Ghergu, Nikos I. Kavallaris, Yasuhito Miyamoto

In this work, we present a novel stationary Gierer-Meinhardt system incorporating non-local proliferation rates, defined as follows: $$ \begin{cases} \displaystyle -Δu+λu=\frac{J*u…

math.AP2025

Infinite multiplicity of positive solutions of an inhomogeneous supercritical elliptic equation on $R^{N}$

Sho Katayama, Yasuhito Miyamoto

We are concerned with positive radial solutions of the inhomogeneous elliptic equation $Δ u + K (∣ x ∣) u^{p} + μ f (∣ x ∣) = 0$ on $R^{N}$ , where $N \geq 3$ , $μ > 0$ and $K$ and $f$ are nonnega…

math.AP2025

Exact solutions describing very slow layer oscillations in a shadow reaction-diffusion system

Shin-Ichiro Ei, Yasuhito Miyamoto, Tatsuki Mori

We show in a rigorous way that a stable internal single-layer stationary solution is destabilized by the Hopf bifurcation as the time constant exceeds a certain critical value. Mor…

math.AP2024

Threshold property of a singular stationary solution for semilinear heat equations with exponential growth

Kotaro Hisa, Yasuhito Miyamoto

Let $N \geq 3$ . We are concerned with a Cauchy problem of the semilinear heat equation \[ \begin{cases} \partial_tu-Δu=f(u), & x\in\mathbb{R}^N,\ t>0,\\ u(x,0)=u_0(x), & x\in\mathbb{…

math.AP2021

Nonlinear Inequalities with Double Riesz Potentials

Marius Ghergu, Zeng Liu, Yasuhito Miyamoto +1

We investigate the nonnegative solutions to the nonlinear integral inequality $u \geq I_{α} * ((I_{β} * u^{p}) u^{q})$ a.e. in $R^{N}$ , where $α, β \in (0, N)$ , $p, q > 0$ and…

math.AP2021★ 1 cited

Thresholds on growth of nonlinearities and singularity of initial functions for semilinear heat equations

Yasuhito Miyamoto, Masamitsu Suzuki

Let $N \geq 1$ and let $f \in C [0, \infty)$ be a nonnegative nondecreasing function and $u_{0}$ be a possibly singular nonnegative initial function. We are concerned with existence and n…

math.AP2021

Polyharmonic inequalities with nonlocal terms

Marius Ghergu, Yasuhito Miyamoto, Vitaly Moroz

We study the existence and non-existence of classical solutions for inequalities of type $$ \pm Δ^m u \geq \big(Ψ(|x|)*u^p\big)u^q \quad\mbox{ in } {\mathbb R}^N (N\geq 1). $$ Here…

math.AP2020★ 19 cited

The compactness of minimizing sequences for a nonlinear Schrödinger system with potentials

Norihisa Ikoma, Yasuhito Miyamoto

In this paper, we consider the following minimizing problem with two constraints: \[ \inf \left\{ E(u) | u=(u_1,u_2), \ \| u_1 \|_{L^2}^2 = α_1, \ \| u_2 \|_{L^2}^2 = α_2 \right\},…

math.AP2020★ 1 cited

Radial regular and rupture solutions for a MEMS model with fringing field

Marius Ghergu, Yasuhito Miyamoto

We investigate radial solutions for the problem \[ \begin{cases} \displaystyle -ΔU=\frac{λ+δ|\nabla U|^2}{1-U},\; U>0 & \textrm{in}\ B,\\ U=0 & \textrm{on}\ \partial B, \end{cases}…

math.AP2020★ 1 cited

Radial single point rupture solutions for a general MEMS model

Marius Ghergu, Yasuhito Miyamoto

We study the initial value problem $$ \begin{cases} r^{-(γ-1)}\left(r^α|u'|^{β-1}u'\right)'=\frac{1}{f(u)} & \textrm{for}\ 0<r<r_0,\\ u(r)>0 & \textrm{for}\ 0<r<r_0,\\ u(0)=0, \end…

math.AP2020

Fractional semilinear heat equations with singular and nondecaying initial data

Théo Giraudon, Yasuhito Miyamoto

We study integrability conditions for existence and nonexistence of a local-in-time integral solution of fractional semilinear heat equations with rather general growing nonlineari…

math.AP2020★ 1 cited

Structure of the positive radial solutions for the supercritical Neumann problem $ε^{2} Δ u - u + u^{p} = 0$ in a ball

Yasuhito Miyamoto

We are interested in the structure of the positive radial solutions of the supercritical Neumann problem $ε^{2} Δ u - u + u^{p} = 0$ on a unit ball in $R^{N}$ , where $N$ is t…

math.AP2020★ 6 cited

Exact eigenvalues and eigenfunctinos for a one-dimensional Gel'fand problem

Yasuhito Miyamoto, Tohru Wakasa

It is known that every positive solution of a one-dimensional Gel'fand problem can be written explicitly. In this paper we obtain exact expressions of all the eigenvalues and eigen…

math.AP2019★ 4 cited

The Emden-Fowler equation on a spherical cap of $S^{N}$

Atsushi Kosaka, Yasuhito Miyamoto

Let $S^{N} \subset R^{N + 1}$ , $N \geq 3$ , be the unit sphere, and let $S_{Θ} \subset S^{N}$ be a geodesic ball with geodesic radius $Θ \in (0, π)$ . We study the bifurcat…

math.AP2019★ 36 cited

A limit equation and bifurcation diagrams of semilinear elliptic equations with general supercritical growth

Yasuhito Miyamoto

We study radial solutions of the semilinear elliptic equation $Δ u + f (u) = 0$ under rather general growth conditions on $f$ . We construct a radial singular solution and study the inter…

math.AP2019★ 9 cited

A doubly critical semilinear heat equation in the $L^{1}$ space

Yasuhito Miyamoto

We study the existence and nonexistence of a Cauchy problem of the semilinear heat equation $\partial_{t} u = Δ u + ∣ u ∣^{p - 1} u$ in $R^{N} \times (0, T)$ , $u (x, 0) = ϕ (x)$ in $\mathbb{R}^N…

math.AP2018

Multiplicity of bounded solutions to the $k$ -Hessian equation with a Matukuma-type source

Yasuhito Miyamoto, Justino Sanchez, Vicente Vergara

The aim of this paper is to deal with the $k$ -Hessian counterpart of the Laplace equation involving a nonlinearity studied by Matukuma. Namely, our model is the problem \begin{equa…

math.AP2015★ 1 cited

Infinitely many nonradial singular solutions of $Δ u + e^{u} = 0$ in $R^{N} \ {0}$ , $4 \leq N \leq 10$

Yasuhito Miyamoto

We construct countably infinitely many nonradial singular solutions of the problem \[ Δu+e^u=0\ \ \textrm{in}\ \ \mathbb{R}^N\backslash\{0\},\ \ 4\le N\le 10 \] of the form \[ u(r,…

Monotonicity of the bifurcation curve for supercritical elliptic problems in the borderline dimension N=10

Classification of the structures of stable radial solutions for semilinear elliptic equations in RN

Non-uniqueness of positive solutions for supercritical semilinear heat equations without scale invariance

The Gierer-Meinhardt system in the entire space with non-local proliferation rates

Infinite multiplicity of positive solutions of an inhomogeneous supercritical elliptic equation on RN

Exact solutions describing very slow layer oscillations in a shadow reaction-diffusion system

Threshold property of a singular stationary solution for semilinear heat equations with exponential growth

Nonlinear Inequalities with Double Riesz Potentials

Thresholds on growth of nonlinearities and singularity of initial functions for semilinear heat equations

Polyharmonic inequalities with nonlocal terms

The compactness of minimizing sequences for a nonlinear Schrödinger system with potentials

Radial regular and rupture solutions for a MEMS model with fringing field

Radial single point rupture solutions for a general MEMS model

Fractional semilinear heat equations with singular and nondecaying initial data

Structure of the positive radial solutions for the supercritical Neumann problem ε2Δu−u+up=0 in a ball

Exact eigenvalues and eigenfunctinos for a one-dimensional Gel'fand problem

The Emden-Fowler equation on a spherical cap of SN

A limit equation and bifurcation diagrams of semilinear elliptic equations with general supercritical growth

A doubly critical semilinear heat equation in the L1 space

Multiplicity of bounded solutions to the k-Hessian equation with a Matukuma-type source

Infinitely many nonradial singular solutions of Δu+eu=0 in RN\{0}, 4≤N≤10

Monotonicity of the bifurcation curve for supercritical elliptic problems in the borderline dimension $N = 10$

Classification of the structures of stable radial solutions for semilinear elliptic equations in $R^{N}$

Infinite multiplicity of positive solutions of an inhomogeneous supercritical elliptic equation on $R^{N}$

Structure of the positive radial solutions for the supercritical Neumann problem $ε^{2} Δ u - u + u^{p} = 0$ in a ball

The Emden-Fowler equation on a spherical cap of $S^{N}$

A doubly critical semilinear heat equation in the $L^{1}$ space

Multiplicity of bounded solutions to the $k$ -Hessian equation with a Matukuma-type source

Infinitely many nonradial singular solutions of $Δ u + e^{u} = 0$ in $R^{N} \ {0}$ , $4 \leq N \leq 10$