Results 61 to 70 of about 232 (187)

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

An Improved Fountain Theorem and Its Application

Advanced Nonlinear Studies, 2017
The main aim of the paper is to prove a fountain theorem without assuming the τ-upper semi-continuity condition on the variational functional. Using this improved fountain theorem, we may deal with more general strongly indefinite elliptic problems with ...
Gu Long-Jiang, Zhou Huan-Song
doaj   +1 more source

An Adaptive Multigrid Method for Semilinear Elliptic Equations

East Asian Journal on Applied Mathematics, 2019
Summary: An adaptive multigrid method for semilinear elliptic equations based on adaptive multigrid methods and on multilevel correction methods is developed. The solution of a semilinear problem is reduced to a series of linearised elliptic equations on the sequence of adaptive finite element spaces and semilinear elliptic problems on a very low ...
Xu, Fei, Huang, Qiumei, Chen, Shuangshuang, Bing, Tao   +3 more
openaire   +2 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

An abstract approximate controllability result and applications to elliptic and parabolic systems with dynamic boundary conditions

Electronic Journal of Differential Equations, 2001
In this paper we prove an approximate controllability result for an abstract semilinear evolution equation in a Hilbert space and we obtain as consequences the approximate controllability for some classes of elliptic and parabolic problems subjected to ...
Ioan Bejenaru, Jesus Ildefonso Diaz, Ioan I. Vrabie   +2 more
doaj  

Arithmetic Satake compactifications and algebraic Drinfeld modular forms

Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.
Abstract In this article, we construct the arithmetic Satake compactification of the Drinfeld moduli schemes of arbitrary rank over the ring of integers of any global function field away from the level structure, and show that the universal family extends uniquely to a generalized Drinfeld module over the compactification.
Urs Hartl, Chia‐Fu Yu
wiley   +1 more source

Large solutions of semilinear elliptic equations with nonlinear gradient terms

International Journal of Mathematics and Mathematical Sciences, 1999
We show that large positive solutions exist for the equation (P±):Δu±|∇u|q=p(x)uγ in Ω⫅RN(N≥3) for appropriate choices of γ>1,q>0 in which the domain Ω is either bounded or equal to RN.
Alan V. Lair, Aihua W. Wood
doaj   +1 more source

Concentration and dynamic system of solutions for semilinear elliptic equations

Electronic Journal of Differential Equations, 2003
In this article, we use the concentration of solutions of the semilinear elliptic equations in axially symmetric bounded domains to prove that the equation has three positive solutions. One solution is y-symmetric and the other are non-axially symmetric.
Tsung-fang Wu
doaj  

Multiple Positive Solutions for Semilinear Elliptic Equations with Sign-Changing Weight Functions in ℝ𝑁

Abstract and Applied Analysis, 2011
Existence and multiplicity of positive solutions for the following semilinear elliptic equation: −Δ𝑢+𝑢=𝑎(𝑥)|𝑢|𝑝−2𝑢+𝜆𝑏(𝑥)|𝑢|𝑞−2𝑢 in ℝ𝑁, 𝑢∈𝐻1(ℝ𝑁), are established, where 𝜆>0 ...
Tsing-San Hsu
doaj   +1 more source

An inverse boundary-value problem for semilinear elliptic equations

Electronic Journal of Differential Equations, 2010
We show that in dimension two or greater, a certain equivalence class of the scalar coefficient $a(x,u)$ of the semilinear elliptic equation $Delta u,+a(x,u)=0$ is uniquely determined by the Dirichlet to Neumann map of the equation on a bounded ...
Ziqi Sun
doaj