Results 21 to 30 of about 838 (110)

ON THE VOLTERRA-STIELTJES INTEGRAL EQUATION AND AXIOMATIC MEASURES OF WEAK NONCOMPACTNESS

International Journal of Apllied Mathematics, 2019
In this note, we will use a compactness type condition in connection with the weak topology to prove the existence of weakly continuous solutions for a functional integral equation of Volterra-Stieltjes type in nonreflexive Banach spaces.
A.A.H. Abd El-Mwla
semanticscholar   +1 more source

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

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

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 of Fractional Order Differential Equations via Volterra-Stieltjes Integral Operator

, 2017
The fractional derivative of the Riemann-Liouville and Caputo types played an important role in the development of the theory of fractional derivatives, integrals and for its applications in pure mathematics ([18], [21]).
A. El-Sayed, W. El-Sayed, A. El-Mowla
semanticscholar   +1 more source

Existence of an unbounded branch of the set of solutions for Neumann problems involving the p(x)-Laplacian

Boundary Value Problems, 2014
We are concerned with the following nonlinear problem: −div(w(x)|∇u|p(x)−2∇u)+|u|p(x)−2u=μg(x)|u|p(x)−2u+f(λ,x,u,∇u) in Ω, ∂u∂n=0 on ∂ Ω, which is subject to a Neumann boundary condition, provided that μ is not an eigenvalue of the p(x)-Laplacian.
Byung-Hoon Hwang, Seung Dae Lee, Yun-Ho Kim   +2 more
semanticscholar   +2 more sources

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

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

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

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