Results 71 to 80 of about 15,562 (203)

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

Semilinear elliptic equations admitting similarity transformations

Journal of Functional Analysis, 2014
In this paper we study the equation $- u+ ^{-( +2)}h( ^ u)=0$ in a smooth bounded domain $ $ where $ (x)=\textrm{dist}\,(x,\partial )$, $ >0$ and $h$ is a non-decreasing function which satisfies Keller-Osserman condition. We introduce a condition on $h$ which implies that the equation is subcritical, i.e.
Bhakta, Mousomi, Marcus, Moshe
openaire   +2 more sources

On the wave turbulence theory of 2D gravity waves, I: Deterministic energy estimates

Communications on Pure and Applied Mathematics, Volume 78, Issue 2, Page 211-322, February 2025.
Abstract Our goal in this paper is to initiate the rigorous investigation of wave turbulence and derivation of wave kinetic equations (WKEs) for water waves models. This problem has received intense attention in recent years in the context of semilinear models, such as Schrödinger equations or multidimensional KdV‐type equations. However, our situation
Yu Deng, Alexandru D. Ionescu, Fabio Pusateri   +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

Infinitely many solutions for semilinear nonlocal elliptic equations under noncompact settings [PDF]

, 2015
In this paper, we study a class of semilinear nonlocal elliptic equations posed on settings without compact Sobolev embedding. More precisely, we prove the existence of infinitely many solutions to the fractional Brezis-Nirenberg problems on bounded ...
Choi, Woocheol, Seok, Jinmyoung
core  

Hermite solution for a new fractional inverse differential problem

Mathematical Methods in the Applied Sciences, Volume 48, Issue 3, Page 3811-3824, February 2025.
Mathematics, mathematical modeling of real systems, and mathematical and computer methodologies aimed at the qualitative and quantitative study of real physical systems interact in a nontrivial way. This work aims to examine a new class of inverse problems for a fractional partial differential equation with order fractional 0<ρ≤1$$ 0<\rho \le 1 ...
Mohammed Elamine Beroudj, Abdelaziz Mennouni, Carlo Cattani   +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  

Dissipative Gradient Nonlinearities Prevent δ$\delta$‐Formations in Local and Nonlocal Attraction–Repulsion Chemotaxis Models

Studies in Applied Mathematics, Volume 154, Issue 2, February 2025.
ABSTRACT We study a class of zero‐flux attraction–repulsion chemotaxis models, characterized by nonlinearities laws for the diffusion of the cell density u$u$, the chemosensitivities and the production rates of the chemoattractant v$v$ and the chemorepellent w$w$. In addition, a source involving also the gradient of u$u$ is incorporated.
Tongxing Li, Daniel Acosta‐Soba, Alessandro Columbu, Giuseppe Viglialoro   +3 more
wiley   +1 more source