Results 41 to 50 of about 15,562 (203)
On the principle of linearized stability for quasilinear evolution equations in time‐weighted spaces
Mathematische Nachrichten, Volume 298, Issue 12, Page 3939-3959, December 2025.Abstract Quasilinear (and semilinear) parabolic problems of the form v′=A(v)v+f(v)$v^{\prime }=A(v)v+f(v)$ with strict inclusion dom(f)⊊dom(A)$\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)$ of the domains of the function v↦f(v)$v\mapsto f(v)$ and the quasilinear part v↦A(v)$v\mapsto A(v)$ are considered in the framework of time‐weighted function spaces ...
Bogdan‐Vasile Matioc +2 more
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Uniqueness of singular solution of semilinear elliptic equation
, 2010 In this paper, we study asymptotic behavior of solution near 0 for a class of elliptic problem.
Baishun, Lai, Qing, Luo
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Weak solutions for a singular beam equation
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 105, Issue 12, December 2025.Abstract This paper deals with a dynamic Gao beam of infinite length subjected to a moving concentrated Dirac mass. Under appropriate regularity assumptions on the initial data, the problem possesses a weak solution which is obtained as the limit of a sequence of solutions of regularized problems.
Olena Atlasiuk +2 more
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Mathematical Methods in the Applied Sciences, Volume 48, Issue 16, Page 14890-14908, 15 November 2025.ABSTRACT We analyze nonlinear degenerate coupled partial differential equation (PDE)‐PDE and PDE‐ordinary differential equation (ODE) systems that arise, for example, in the modelling of biofilm growth. One of the equations, describing the evolution of a biomass density, exhibits degenerate and singular diffusion.
K. Mitra, S. Sonner
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A semilinear elliptic problem involving nonlinear boundary condition and sign-changing potential
Electronic Journal of Differential Equations, 2006 In this paper, we study the multiplicity of nontrivial nonnegative solutions for a semilinear elliptic equation involving nonlinear boundary condition and sign-changing potential.
Tsung-Fang Wu
doaj
Generalized Harnack inequality for semilinear elliptic equations
, 2016 This paper is concerned with semilinear equations in divergence form \[ \diver(A(x)Du) = f(u) \] where $f :\R \to [0,\infty)$ is nondecreasing. We prove a sharp Harnack type inequality for nonnegative solutions which is closely connected to the classical
Julin, Vesa
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Existence of Weak Solutions for a Degenerate Goursat‐Type Linear Problem
Mathematical Methods in the Applied Sciences, Volume 48, Issue 15, Page 14334-14341, October 2025.ABSTRACT For a generalization of the Gellerstedt operator with mixed‐type Dirichlet boundary conditions to a suitable Tricomi domain, we prove the existence and uniqueness of weak solutions of the linear problem and for a generalization of this problem.
Olimpio Hiroshi Miyagaki +2 more
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Large versus bounded solutions to sublinear elliptic problems
, 2018 Let $L $ be a second order elliptic operator with smooth coefficients defined on a domain $\Omega \subset \mathbb{R}^d$ (possibly unbounded), $d\geq 3$.
Damek, Ewa, Ghardallou, Zeineb
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Semilinear fractional elliptic equations involving measures
Journal of Differential Equations, 2014 We study the existence of weak solutions of (E) $ (- )^ u+g(u)= $ in a bounded regular domain $ $ in $\R^N (N\ge2)$ which vanish on $\R^N\setminus $, where $(- )^ $ denotes the fractional Laplacian with $ \in(0,1)$, $ $ is a Radon measure and $g$ is a nondecreasing function satisfying some extra hypothesis.
Chen, Huyuan, Véron, Laurent
openaire +3 more sources
Construction of blow‐up solutions for Liouville systems
Proceedings of the London Mathematical Society, Volume 131, Issue 4, October 2025.Abstract We study the following Liouville system defined on a flat torus −Δui=∑j=1naijρjhjeuj∫Ωhjeuj−1,uj∈Hper1(Ω)fori∈I={1,…,n},$$\begin{equation*} {\left\lbrace \def\eqcellsep{&}\begin{array}{lr}-\Delta u_i=\sum _{j=1}^n a_{ij}\rho _j{\left(\frac{h_j e^{u_j}}{\int _\Omega h_j e^{u_j}}-1\right)},\\[3pt] u_j\in H_{per}^1(\Omega)\mbox{ for }i\in I ...
Zetao Cheng, Haoyu Li, Lei Zhang
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