Results 51 to 60 of about 15,562 (203)

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  

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

Comparison results for semilinear elliptic equations via Picone-type identities

Electronic Journal of Differential Equations, 2009
By means of a Picone's type identity, we prove uniqueness and oscillation of solutions to an elliptic semilinear equation with Dirichlet boundary conditions.
Tadie
doaj  

Higher-dimensional solutions for a nonuniformly elliptic equation

, 2013
We prove $m$-dimensional symmetry results, that we call $m$-Liouville theorems, for stable and monotone solutions of the following nonuniformly elliptic equation \begin{eqnarray*}\label{mainequ} - div(\gamma(\mathbf x') \nabla u(\mathbf x)) =\lambda ...
Fazly, Mostafa
core   +1 more source

Asymptotic solutions of semilinear elliptic equations

Journal of Mathematical Analysis and Applications, 1984
Semilinear elliptic equations of the form \(Lu\equiv \Delta u-p(| x|)u+uf(x,u)=0\) are considered in exterior domains in \({\mathbb{R}}^ n\) for \(n\geq 2\). Both necessary and sufficient conditions are established for such equations to have positive solutions with prescribed asymptotic behavior as \(| x| \to \infty\).
Kreith, Kurt, Swanson, Charles A
openaire   +1 more source

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

Asymptotic behavior and uniqueness of boundary blow-up solutions to elliptic equations

Electronic Journal of Qualitative Theory of Differential Equations, 2015
In this paper, under some structural assumptions of weight function $b(x)$ and nonlinear term $f(u)$, we establish the asymptotic behavior and uniqueness of boundary blow-up solutions to semilinear elliptic equations \begin{equation*} \begin{cases ...
Qiaoyu Tian, Yonglin Xu
doaj   +1 more source

Forward uncertainty quantification in random differential equation systems with delta‐impulsive terms: Theoretical study and applications

Mathematical Methods in the Applied Sciences, Volume 48, Issue 7, Page 7609-7629, 15 May 2025.
This contribution aims at studying a general class of random differential equations with Dirac‐delta impulse terms at a finite number of time instants. Our approach directly addresses calculating the so‐called first probability density function, from which all the relevant statistical information about the solution, a stochastic process, can be ...
Vicente J. Bevia, Juan C. Cortés, Rafael J. Villanueva   +2 more
wiley   +1 more source

On Singular Semilinear Elliptic Equations

, 1991
For the semilinear elliptic equation Δu + p(x)u⁻ʸ = 0, x ∈ Rⁿ, n ≥ 3, γ > 0, we show via the barrier method the existence of a positive entire solution behaving like |x|²⁻ⁿ near ∞.
openaire   +3 more sources

The free boundary for semilinear problems with highly oscillating singular terms

Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.
Abstract We investigate general semilinear (obstacle‐like) problems of the form Δu=f(u)$\Delta u = f(u)$, where f(u)$f(u)$ has a singularity/jump at {u=0}$\lbrace u=0\rbrace$ giving rise to a free boundary. Unlike many works on such equations where f$f$ is approximately homogeneous near {u=0}$\lbrace u = 0\rbrace$, we work under assumptions allowing ...
Mark Allen, Dennis Kriventsov, Henrik Shahgholian   +2 more
wiley   +1 more source