Results 51 to 60 of about 232 (187)

Properties of the least action level and the existence of ground state solution to fractional elliptic equation with harmonic potential [PDF]

Opuscula Mathematica
In this article we consider the following fractional semilinear elliptic equation \[(-\Delta)^su+|x|^2u =\omega u+|u|^{2\sigma}u \quad \text{ in } \mathbb{R}^N,\] where \(s\in (0,1)\), \(N\gt 2s\), \(\sigma\in (0,\frac{2s}{N-2s})\) and \(\omega\in (0 ...
César E. Torres Ledesma, Hernán C. Gutierrez, Jesús A. Rodríguez, Manuel M. Bonilla   +3 more
doaj   +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

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

Super and subsolutions for elliptic equations on all of ℝn

International Journal of Mathematics and Mathematical Sciences, 2002
By construction sub and supersolutions for the following semilinear elliptic equation −△u(x)=λg(x)f(u(x)), x∈ℝn which arises in population genetics, we derive some results about the theory of existence of solutions as well as asymptotic properties of the
G. A. Afrouzi, H. Ghasemzadeh
doaj   +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

Solutions to nonlinear elliptic equations with a nonlocal boundary condition

Electronic Journal of Differential Equations, 2002
We study an elliptic equation and its evolution problem on a bounded domain with nonlocal boundary conditions. Eigenvalue problems, existence, and dynamic behavior of solutions for linear and semilinear equations are investigated.
Yuandi Wang
doaj  

Multiple Positive Solutions for Semilinear Elliptic Equations in ℝ𝑁 Involving Concave-Convex Nonlinearities and Sign-Changing Weight Functions

Abstract and Applied Analysis, 2010
We study the existence and multiplicity of positive solutions for the following semilinear elliptic equation −Δ𝑢+𝑢=𝜆𝑎(𝑥)|𝑢|𝑞−2𝑢+𝑏(𝑥)|𝑢|𝑝−2𝑢 in ℝ𝑁, 𝑢∈𝐻1(ℝ𝑁), where 𝜆>0 ...
Tsing-San Hsu, Huei-Li Lin
doaj   +1 more source

Local versus nonlocal elliptic equations: short-long range field interactions

Advances in Nonlinear Analysis, 2020
In this paper we study a class of one-parameter family of elliptic equations which combines local and nonlocal operators, namely the Laplacian and the fractional Laplacian.
Cassani Daniele, Vilasi Luca, Wang Youjun   +2 more
doaj   +1 more source