Results 31 to 40 of about 838 (110)

Positivity of the infimum eigenvalue for equations of p(x)-Laplace type in RN

Boundary Value Problems, 2013
We study the following elliptic equations with variable exponents −div(ϕ(x,|∇u|)∇u)=λf(x,u)in RN. Under suitable conditions on ϕ and f, we show the existence of positivity of the infimum of all eigenvalues for the problem above, and then give an ...
I. Kim, Yun-Ho Kim
semanticscholar   +2 more sources

On the regularity of solutions of the boundary value problem without initial condition for Schrödinger systems in domain with conical points

Boundary Value Problems, 2014
In this paper, we deal with the boundary value problems without initial condition for Schrödinger systems in cylinders. We establish several results on the regularity of the solutions.MSC: 35Q41, 35B65, 35D30.
Nguyen Thi Lien, N. M. Hung
semanticscholar   +2 more sources

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  

ON THE WEAK SOLUTIONS OF THE URYSOHN-STIELTJES FUNCTIONAL INTEGRAL EQUATIONS

, 2018
The analysis of Urysohn-Stieltjes integral operators has been studied in [1]. Here we study the existence of weakly solution of functional integral equations of Urysohn-Stieltjes type and Hammerstien-Stieltjes type in the reflexive Banach space E.
A. El-Sayed, M. M. Al-Fadel
semanticscholar   +1 more source

Existence of an unbounded branch of the set of solutions for equations of p(x)-Laplace type

Boundary Value Problems, 2014
We are concerned with the following nonlinear problem −div(ϕ(x,|∇u|)∇u)=μ|u|p(x)−2u+f(λ,x,u,∇u)in Ω subject to Dirichlet boundary conditions, provided that μ is not an eigenvalue of the p(x)-Laplacian.
Yun-Ho Kim
semanticscholar   +2 more sources

Weak solutions for generalized p-Laplacian systems via Young measures

Moroccan Journal of Pure and Applied Analysis, 2018
We prove the existence of weak solutions to a generalized p-Laplacian systems in degenerate form. The techniques of Young measure for elliptic systems are used to prove the existence result.
Azroul Elhoussine, Balaadich Farah
doaj   +1 more source

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  

Well-posedness and stability analysis for Timoshenko beam system with Coleman-Gurtin's and Gurtin-Pipkin's thermal laws

Open Mathematics, 2023
In this article, the effect of Coleman-Gurtin’s and Gurtin-Pipkin’s thermal laws on the displacement of a Timoshenko beam system with suspenders is studied.
Mukiawa Soh Edwin
doaj   +1 more source

The double and triple bubble problem for stationary varifolds: the convex case [PDF]

arXiv, 2023
We characterize the critical points of the double bubble problem in $\mathbb{R}^n$ and the triple bubble problem in $\mathbb{R}^3$, in the case the bubbles are convex.
arxiv  

MULTIPLE SOLUTIONS FOR A CLASS OF (P1(X), P2(X))-LAPLACIAN PROBLEMS WITH NEUMANN BOUNDARY CONDITIONS

, 2019
In this paper, we study the existence of solutions for a class of nonlinear Neumann problems with variable exponents of the form  −div ( (|∇u|p1(x)−2 + |∇u|p2(x)−2)∇u ) + |u|pmax(x)−2u = λf(x, u) + μg(x, u) in Ω, ∂u ∂ν = 0 on ∂Ω, where Ω ⊂ RN , N ≥ 3
N. T. Chung
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