Results 51 to 60 of about 278 (186)

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, Lina Sophie Schmitz, Christoph Walker   +2 more
wiley   +1 more source

Dirichlet problems for semilinear elliptic equations with a fast growth coefficient on unbounded domains

Electronic Journal of Differential Equations, 2005
When an unbounded domain is inside a slab, existence of a positive solution is proved for the Dirichlet problem of a class of semilinear elliptic equations that are similar either to the singular Emden-Fowler equation or a sublinear elliptic equation ...
Zhiren Jin
doaj  

Existence of nonminimal solutions to an inhomogeneous elliptic equation with supercritical nonlinearity

Advanced Nonlinear Studies, 2023
In our previous paper [K. Ishige, S. Okabe, and T. Sato, A supercritical scalar field equation with a forcing term, J. Math. Pures Appl. 128 (2019), pp.
Ishige Kazuhiro, Okabe Shinya, Sato Tokushi   +2 more
doaj   +1 more source

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, Arnaud Heibig, Adrien Petrov   +2 more
wiley   +1 more source

Separation Property of Solutions for a Semilinear Elliptic Equation [PDF]

Journal of Differential Equations, 2000
The authors consider the problem of finding a positive solution \(u\) of the differential equation \(\Delta u + K(|x|)u^p = 0\) in \(\mathbb{R}^n\setminus \{0\}\). Here \(K\) is a given function which is Hölder continuous in \(\mathbb{R}^n\setminus \{0\}\). Many authors (often in collaboration with Li) have studied this problem under various hypotheses
Liu, Yi, Li, Yi, Deng, Yinbin
openaire   +2 more sources

Quasilinear Degenerate Evolution Systems Modelling Biofilm Growth: Well‐Posedness and Qualitative Properties

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
wiley   +1 more source

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, Carlos Alberto Reyes Peña, Rodrigo da Silva Rodrigues   +2 more
wiley   +1 more source

Parallelization of Faber Polynomial Based Propagators for Laser Applications

International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Volume 38, Issue 4, July/August 2025.
ABSTRACT In order to simulate a laser system, the evaluation of a complex semilinear master equation is needed, including the description of the wave propagation by Maxwell's equations and appropriate rate equations. The denser the spatial discretization, the slower the computation time of the time‐dependent propagator.
Wladimir Plotnikov, Dirk Schulz
wiley   +1 more source

Uniqueness of positive solutions for cooperative Hamiltonian elliptic systems

Electronic Journal of Differential Equations, 2016
The uniqueness of positive solution of a semilinear cooperative Hamiltonian elliptic system with two equations is proved for the case of sublinear and superlinear nonlinearities. Implicit function theorem, bifurcation theory, and ordinary differential
Junping Shi, Ratnasingham Shivaji
doaj  

Conformal metrics of constant scalar curvature with unbounded volumes

Proceedings of the London Mathematical Society, Volume 131, Issue 1, July 2025.
Abstract For n⩾25$n\geqslant 25$, we construct a smooth metric g∼$\tilde{g}$ on the standard n$n$‐dimensional sphere Sn$\mathbb {S}^n$ such that there exists a sequence of smooth metrics {g∼k}k∈N$\lbrace \tilde{g}_k\rbrace _{k\in \mathbb {N}}$ conformal to g∼$\tilde{g}$ where each g∼k$\tilde{g}_k$ has scalar curvature Rg∼k≡1$R_{\tilde{g}_k}\equiv 1 ...
Liuwei Gong, Yanyan Li
wiley   +1 more source