Results 21 to 30 of about 1,473 (91)

Infinitely many radial and non-radial sign-changing solutions for Schrödinger equations

Advances in Nonlinear Analysis, 2022
In the present paper, a class of Schrödinger equations is investigated, which can be stated as −Δu+V(x)u=f(u),    x∈ℝN.- \Delta u + V(x)u = f(u),\;\;\;\;x \in {{\rm{\mathbb R}}^N}.
Li Gui-Dong, Li Yong-Yong, Tang Chun-Lei
doaj   +1 more source

Maximum principle for stable operators [PDF]

arXiv, 2022
We prove a weak maximum principle for nonlocal symmetric stable operators. This includes the fractional Laplacian. The main focus of this work is the regularity of the considered function.
arxiv  

Combined effects of Choquard and singular nonlinearities in fractional Kirchhoff problems

Advances in Nonlinear Analysis, 2020
The aim of this paper is to study the existence and multiplicity of solutions for a class of fractional Kirchho problems involving Choquard type nonlinearity and singular nonlinearity.
Wang Fuliang, Hu Die, Xiang Mingqi
doaj   +1 more source

Equivalence between a time-fractional and an integer-order gradient flow: The memory effect reflected in the energy

Advances in Nonlinear Analysis, 2022
Time-fractional partial differential equations are nonlocal-in-time and show an innate memory effect. Previously, examples like the time-fractional Cahn-Hilliard and Fokker-Planck equations have been studied.
Fritz Marvin, Khristenko Ustim, Wohlmuth Barbara   +2 more
doaj   +1 more source

Three weak solutions for a Neumann elliptic equations involving the p→(x)\vec p\left( x \right)-Laplacian operator

Nonautonomous Dynamical Systems, 2020
The aim of this paper is to establish the existence of at least three weak solutions for the following elliptic Neumann problem {-Δp→(x)u+α(x)|u|p0(x)-2u=λf(x,u)inΩ,∑i=1N|∂u∂xi|pi(x)-2∂u∂xiγi=0on∂Ω,\left\{ {\matrix{ { - {\Delta _{\vec p\left( x \right)}}
Ahmed Ahmed, Vall Mohamed Saad Bouh Elemine   +1 more
doaj   +1 more source

Least energy sign-changing solutions for a nonlocal anisotropic Kirchhoff type equation

Moroccan Journal of Pure and Applied Analysis, 2022
In this paper, we investigate the existence of sign-changing solutions for the following class of fractional Kirchhoff type equations with potential (1+b[u]α2)((-Δx)αu-Δyu)+V(x,y)u=f(x,y,u),(x,y)∈ℝN=ℝn×ℝm,\left( {1 + b\left[ u \right]_\alpha ^2} \right ...
Rahmani Mohammed, Rahmani Mostafa, Anane Aomar, Massar Mohammed   +3 more
doaj   +1 more source

On the equivalence of viscosity solutions and distributional solutions for the time-fractional diffusion equation [PDF]

arXiv, 2021
We consider an initial-boundary value problem for the time-fractional diffusion equation. We prove the equivalence of two notions of weak solutions, viscosity solutions and distributional solutions.
arxiv  

Weak and stationary solutions to a Cahn–Hilliard–Brinkman model with singular potentials and source terms

Advances in Nonlinear Analysis, 2020
We study a phase field model proposed recently in the context of tumour growth. The model couples a Cahn–Hilliard–Brinkman (CHB) system with an elliptic reaction-diffusion equation for a nutrient.
Ebenbeck Matthias, Lam Kei Fong
doaj   +1 more source

Local Hölder continuity for fractional nonlocal equations with general growth [PDF]

arXiv, 2021
We study generalized fractional $p$-Laplacian equations to prove local boundedness and H\"older continuity of weak solutions to such nonlocal problems by finding a suitable fractional Sobolev-Poincar\'e inquality.
arxiv  

Weak solutions to the Navier-Stokes equations [PDF]

arXiv, 2022
We prove the equivalence of being a Leray-Hopf weak solution to the Navier-Stokes equations in $\mathbb{R}^m, m \ge 3$, to satisfying a well known integral equation. We use this equation to derive some properties of these weak solutions.
arxiv