Differential and Integral Equations
___________________________________________________________________________________________
Differential and Integral Equations
Volume 38, Numbers 5-6, May/June 2025
Smooth subsolutions of the discounted Hamilton-Jacobi equations
Xiyao Huang, Liang Jin, Jianlu Zhang, and Kai Zhao
Differential and Integral Equations, Volume 38, Number 5/6 (2025), 275-296
Asymptotic stability of one-dimensional compressible viscous and heat-conducting $p$-th micropolar fluid
Lan Huang, Chongchong Li, Xingjie Yan, and Xinguang Yang
Differential and Integral Equations, Volume 38, Number 5/6 (2025), 297-326
The $H^1$-subcritical and critical NLS with time-oscillating coefficients
Mi-Ran Choi and Dugyu Kim
Differential and Integral Equations, Volume 38, Number 5/6 (2025), 327-352
Semilinear Klein-Gordon equation in space-time of black hole which is gaining mass in the universe with accelerating expansion
Karen Yagdjian and Anahit Galstian
Differential and Integral Equations, Volume 38, Number 5/6 (2025), 353-398
Stability for a nonlinear second order ODE with coefficient functions in $W^{1,1}_{\text{loc}}(0,\infty)$
Gheorghe Moroşanu and Cristian Vladimirescu
Differential and Integral Equations, Volume 38, Number 5/6 (2025), 399-416
To appear in the next issue
Volume 38, Numbers 7-8, July/August 2025
Ground state solutions for the nonlinear problem involving
exponential form of Born-Infeld-like
Bingbing Dai and Ruifeng Zhang
Differential and Integral Equations, Volume 38, Number 7/8 (2025), 417-434
Abstract:
In this paper, we investigate dynamical properties in
framework of a quasilinear problem in N-dimensional
space descended from the Born-Infeld-like nonlinear
electromagnetic fields. We establish the existence
of the radial ground state solutions of the quasilinear
problem involving exponential model based on
Born-Infeld theory via dynamical shooting method and
some new methods. Our results open up an intriguing
perspective for research of other nonlinear systems
in Born-Infeld theory including nonlinear
arcsin-electromagnetic field, power-law
electromagnetic field and so on.
Asymptotic boundary behavior of large solutions to equations
involving infinity Laplacian
Ling Mi and Yuanda Yue
Differential and Integral Equations, Volume 38, Number 7/8 (2025), 435-451
Abstract:
The object of this article is to study
the asymptotic behavior of
the blow-up solutions near the boundary
to the following infinity Laplace equation
$$
\triangle_{\infty}^{h} u
=b(x)f(u), \ x\in \Omega,\ u|_{\partial \Omega}=+\infty,
$$
where
$$
\triangle_{\infty}^{h}u := |Du|^{h-3}\langle D^{2}uDu, Du \rangle
$$
for all $h>1,$
$\Omega$ is a bounded domain with smooth boundary
in $\mathbb R^N$,
$b \in C(\bar{\Omega})$ which is positive
in $\Omega$ and the nonlinearity
$f\in C^{1}(0,\infty)$ is positive increasing.
Existence and asymptotical behavior of solutions for a
fractional logarithmic Schrödinger-Poisson system
Jiaqi Dou, Qi Gao, and Zhengping Wang
Differential and Integral Equations, Volume 38, Number 7/8 (2025), 453-472
Abstract:
We study the following fractional
Schrödinger-Poisson system
\begin{equation}\label{eq:0.1}
\left\{\begin{array}{ll}
(-\Delta)^s u + V(x) u + \lambda\phi (x) u
=\mu u+u\log{u^{2}},\ x\in \mathbb{R}^3, \\
(-\Delta)^s\phi = u^2,
\displaystyle
\ \lim_{|x|\to +\infty}\phi (x)=0,
\end{array}\right.
\end{equation}
where
$s\in (\frac{1}{2},1)$, and
$\mu,\lambda$ are real parameters.
Assuming that
$V\in C(\mathbb{R}^3,\mathbb{R}^+)$ and
$\lim_{|x|\to
+\infty}V(x)=\infty$,
we show that problem
(\ref{eq:0.1}) has a nonzero solution
under suitable assumptions on the parameters
$\lambda$ and
$\mu$. Moreover,
the asymptotical behavior of solutions as
$\lambda\to 0$ has also been discussed.
Poincaré-Perron problem for half-linear ordinary differential equations
Manabu Naito and Hiroyuki Usami
Differential and Integral Equations, Volume 38, Number 7/8 (2025), 473-508
Abstract:
This paper deals with the Poincaré-Perron
problem for the second order half-linear
ordinary differential equation
\[
(\Phi_{\alpha}(u'))' + (a_{1} + f_{1}(t))
\Phi_{\alpha}(u') + (a_{2} + f_{2}(t))\Phi_{\alpha}(u) = 0,
\]
where
$\Phi_{\alpha}(u) = |u|^{\alpha}\mathrm{sgn}\, u$
with
$\alpha > 0$, and
$a_{1}$ and
$a_{2}$ are real constants, and
$f_{1}(t)$ and
$f_{2}(t)$ are real-valued continuous functions on
$[t_{0},\infty)$.
It is assumed that
$\alpha|\lambda|^{\alpha + 1}
+ a_{1}\Phi_{\alpha}(\lambda) + a_{2} = 0$
has distinct real roots
$\lambda_{1}$ and
$\lambda_{2}$.
Then it is possible to obtain a necessary and
sufficient condition for the existence of
nonoscillatory solutions
$u_{i}(t)$ which satisfy
$u_{i}'(t)/u_{i}(t) \to \lambda_{i}$ as
$t \to \infty$ ($i = 1, 2$).
It is also shown that, in this case,
any nontrivial solution
$u(t)$ satisfies
$u'(t)/u(t) \to \lambda_{1}$ or
$\lambda_{2}$ as
$t \to \infty$.
The classical results for linear equations
($\alpha = 1$) by Hartman-Wintner
and the recent results by \v{R}eh\'{a}k,
Naito-Usami, Luey-Usami are unified
and generalized to the above equation.
Analyticity in space-time of solutions to evolution equations
with multilinear operators based on maximal regularity
Kei Noda
Differential and Integral Equations, Volume 38, Number 7/8 (2025), 509-536
Abstract:
Space-time analyticity for evolution equations with
nonlinear term represented by multilinear operators
is considered via the parameter trick.
By extending the case of bilinear operators in
the previous work, we obtain
space-time analyticity for the equations
of Fujita type.
To appear in the next issue
Volume 38, Numbers 9-10, September/October 2025
Normalized solutions for critical Kirchhoff-Schrödinger-Poisson
systems in the Heisenberg group
Lifeng Guo and Sihua Liang
Differential and Integral Equations, Volume 38, Number 9/10 (2025), 537-554
Abstract:
In this paper, we consider the existence
and multiplicity of normalized
solutions for critical Kirchhoff-Possion
system involving
$p$-sub-Laplacian in the Heisenberg group.
Under suitable assumptions, combined with
the truncation technique, the
concentration-compactness principle, the
genus theory, we obtain
the existence and multiplicity of the
normalized solutions in the
$L^p$-subcritical case. To some extent,
we extend the results of [19, 30].
Moreover, the result of the paper is
completely new in the Euclidean case.
Scattering for the dispersion managed nonlinear
Schrödinger equation
Mi-Ran Choi, Kiyeon Lee, and Young-Ran Lee
Differential and Integral Equations, Volume 38, Number 9/10 (2025), 555-576
Abstract:
We consider the dispersion managed nonlinear
Schrödinger equations with quintic and
cubic nonlinearities in one and two dimensions,
respectively. We prove the global
well-posedness and scattering in $L_x^2$
for small initial data employing the
$U^p$ and $V^p$ spaces.
The incompressible von Kármán theory for thin pre-strained plates
Hui Li
Differential and Integral Equations, Volume 38, Number 9/10 (2025), 577-594
Abstract:
We derive a new version of the von Kármán energy
and the corresponding Euler-Lagrange equations,
in the context of thin pre-strained plates, under
the condition of incompressibility relative to
the given pre-strain. Our derivation uses the theory of
$\Gamma$-convergence in the calculus of variations,
building on prior techniques in
[6] and [21].
On a diffusion equation with rupture
Yoshikazu Giga and Yuki Ueda
Differential and Integral Equations, Volume 38, Number 9/10 (2025), 595-618
Abstract:
We propose a model to describe an evolution of
a bubble cluster with rupture.
In a special case, the equation is reduced to
a single parabolic equation with evaporation for
the thickness of a liquid layer covering bubbles.
If the liquid layer becomes thinner than a given
threshold value, we call a rupture occurs.
Under assumptions so that the rupture occurs only
in a fixed interval of a bubble,
we prove that the rupture occurs at infinitely many
times and there exists a periodic-in-time solution.
Numerical tests indicate that there may not
exist a periodic solution if such an
assumption is violated.
On the Strichartz estimate for many body
Schrödinger equations on Euclidean cylinder
Han Wang and Zehua Zhao
Differential and Integral Equations, Volume 38, Number 9/10 (2025), 619-641
Abstract:
In this short paper, we study the Strichartz
estimates for many body Schrödinger
equations (MBSE) on Euclidean cylinder
(i.e., on semiperiodic space
$\mathbb{R}\times \mathbb{T}$,
which is also known as a specific type
of waveguide manifold), provided that
interaction potentials are small enough
(depending on the number of the particles
and the universal constants, not on the
initial data).
We will recover the `$L^4_{t,x}$'-type
Strichartz estimate as in the standard
Schrödinger case (Takaoka-Tzvetkov [35]).
This result extends the result of
Hong
[20] to the
Euclidean cylinder case. From another aspect,
this also extends [35]'s
estimate to the many body case.
This result can be also compared with [44]
which also studies Strichartz estimates
for many body Schrödinger equations
on waveguide manifolds. Moreover,
we include a well-posedness result for
the nonlinear case. At last, we discuss
two more related cases: the
three-body-interaction case and the
fourth-order many body Schrödinger equation case.
Copyright © 2025 Khayyam Publishing, Inc.
