Results 91 to 100 of about 93,033 (295)
A Fibering Map Approach for a Laplacian System With Sign-Changing Weight Function [PDF]
, 2014 We prove the existence of at least two positive solutions for the Laplacian system(E?)On a bounded region by using the Nehari manifold and the fibering maps associated with the Euler functional for the ...
Kazemipoor, Seyyed Sadegh +1 more
core
Generalized Harnack inequality for semilinear elliptic equations
, 2016 This paper is concerned with semilinear equations in divergence form \[ \diver(A(x)Du) = f(u) \] where $f :\R \to [0,\infty)$ is nondecreasing. We prove a sharp Harnack type inequality for nonnegative solutions which is closely connected to the classical
Julin, Vesa
core +1 more source
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 +2 more
wiley +1 more source
Semilinear fractional elliptic equations with gradient nonlinearity involving measures [PDF]
, 2013 We study the existence of solutions to the fractional elliptic equation (E1) $(-\Delta)^\alpha u+\epsilon g(|\nabla u|)=\nu $ in a bounded regular domain $\Omega$ of $\R^N (N\ge2)$, subject to the condition (E2) $u=0$ in $\Omega^c$, where $\epsilon=1$ or
Chen, Huyuan, Veron, Laurent
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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$$ 0<\rho \le 1 ...
Mohammed Elamine Beroudj +2 more
wiley +1 more source
Studies in Applied Mathematics, Volume 154, Issue 2, February 2025.ABSTRACT We study a class of zero‐flux attraction–repulsion chemotaxis models, characterized by nonlinearities laws for the diffusion of the cell density u$u$, the chemosensitivities and the production rates of the chemoattractant v$v$ and the chemorepellent w$w$. In addition, a source involving also the gradient of u$u$ is incorporated.
Tongxing Li +3 more
wiley +1 more source
Uniqueness of positive solutions for cooperative Hamiltonian elliptic systems
Electronic Journal of Differential Equations, 2016 The uniqueness of positive solution of a semilinear cooperative Hamiltonian elliptic system with two equations is proved for the case of sublinear and superlinear nonlinearities. Implicit function theorem, bifurcation theory, and ordinary differential
Junping Shi, Ratnasingham Shivaji
doaj
A Liouville theorem for ancient solutions to a semilinear heat equation and its elliptic counterpart
, 2020 We establish the nonexistence of nontrivial ancient solutions to the nonlinear heat equation $u_t=\Delta u+|u|^{p-1}u$ which are smaller in absolute value than the self-similar radial singular steady state, provided that the exponent $p$ is strictly ...
Sourdis, Christos
core
Elliptic equations involving general subcritical source nonlinearity and measures [PDF]
, 2014 In this article, we study the existence of positive solutions to elliptic equation (E1) $$(-\Delta)^\alpha u=g(u)+\sigma\nu \quad{\rm in}\quad \Omega,$$ subject to the condition (E2) $$u=\varrho\mu\quad {\rm on}\quad \partial\Omega\ \ {\rm if}\ \alpha=1 ...
Chen, Huyuan +2 more
core +2 more sources
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