Yasuhito Miyamoto

collaborators

7 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

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.AP2026

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

Yasuhito Miyamoto, YÅ«ki Naito

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

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 -Îu+Î»u=\frac{J…

math.AP2025

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-Îu=f(u), & x\in\mathbb{R}^N,\ t>0,\\ u(x,0)=u_0(x), & x\in\mathbb…

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 $I^ u + K (∣ x ∣) u^{p} + I^¼ f (∣ x ∣) = 0$ on $R^{N}$ , where $N \geq 3$ , $I^¼ > 0$ and $K$ and $f$ are nonn…

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

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

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

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

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

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

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 $R^{N}$