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Multiple sign-changing solutions for semilinear subelliptic Dirichlet problem
Hua Chen, Hong-Ge Chen, Jin-Ning Li, Xin Liao
https://arxiv.org/abs/2510.10120 https://

Multiple sign-changing solutions for semilinear subelliptic Dirichlet problem
We study the following perturbation from symmetry problem for the semilinear subelliptic equation \[ \left\{ \begin{array}{cc} -\triangle_{X} u=f(x,u)+g(x,u) & \mbox{in}~Ω, \\[2mm] u\in H_{X,0}^{1}(Ω),\hfill \end{array} \right. \] where $\triangle_{X}=-\sum_{i=1}^{m}X_{i}^{*}X_{i}$ is the self-adjoint sub-elliptic operator associated with Hörmander vector fields $X=(X_{1},X_{2},\ldots,X_{m})$, $Ω$ is an open bounded subset in $\mathbb{R}^n$, and $H_{X,0}^{1}(Ω)$ denotes the weigh…

Ergodic approach to the study of boundedness of solutions of one type of the first-order semilinear difference equations
Andrii Chaikovskyi, Oleksandr Liubimov
https://arxiv.org/abs/2509.11320

Ergodic approach to the study of boundedness of solutions of one type of the first-order semilinear difference equations
We investigate the sufficient conditions for boundedness of one type of difference equations of the form $x(n+1)=ax(n)+f(x(n)) + y(n), \ n\geq 1$ in critical case $|a|=1$. For this equation the following assumptions are introduced: 1) The function $f: \mathbb{C} \to \mathbb{C}$ and the input sequence $\{y(n)\}_{n\geq1}$ are assumed to be bounded. 2) $\text{Re}\left(\overline{f(ρ\, e^{2πi θ})} \; \cdot ae^{2πi θ}\right)$ converges uniformly on $[0,1) \ni θ$ to some real-val…

Local well-posedness for a class of semilinear Moore-Gibson-Thompson equations with subcritical nonlinearities
Flank D. M. Bezerra, Lu\'is M. Salge
https://arxiv.org/abs/2510.06944

Local well-posedness for a class of semilinear Moore-Gibson-Thompson equations with subcritical nonlinearities
In this paper, we study a class of higher-order semilinear evolution equations inspired by the Moore-Gibson-Thompson model introduced by Dell'Oro, Liverani and Pata (2023), involving strongly elliptic operators of order ($2m$) with homogeneous boundary conditions. The associated unbounded linear operator is a sectorial operator with zero belonging to the resolvent set, allowing the construction of fractional powers spaces, and the analysis of their spectral properties. We prove the local well-p…

Non-autonomous problem for a $2m$-th order semilinear nonlocal parabolic equation
Flank D. M. Bezerra, Silvia Sastre-G\'omez
https://arxiv.org/abs/2507.20257 https://…

Non-autonomous problem for a $2m$-th order semilinear nonlocal parabolic equation
In this paper we consider a $2m$-th order non autonomous quasilinear parabolic equation. Under suitable conditions of growth and regularity for the nonlinear functions present in the model, we prove a result of existence and characterization of pullback attractors. Moreover, we consider an autonomous version from the $2m$-th order non autonomous quasilinear parabolic equation in question.

Infinite BV, large $L^\infty$ solutions of conservation laws are H\"older-stable in $L^2$ in the class of front tracking limits
Geng Chen (University of Kansas), Cooper Faile (The University of Texas at Austin), Sam G. Krupa (\'Ecole normale sup\'erieure)
https://arxiv.org/abs/2507.23645…

Infinite BV, large $L^\infty$ solutions of conservation laws are Hölder-stable in $L^2$ in the class of front tracking limits
We consider hyperbolic systems of conservation laws in one spatial dimension. For any limit of front tracking solutions $v$, and for a general weak solution $u\in L^\infty$ with no BV assumption, we prove the following Hölder-type stability estimate in $L^2$: $$||u(\cdot,τ)-v(\cdot,τ)||_{L^2} \leq K \sqrt{||u( \cdot,0)-v( \cdot,0)||_{L^2}}$$ for all $τ$ without smallness and for a universal constant $K$. Our result holds for all limits of front tr…