Elliptic Equations in R + d with Homogeneous Dirichlet Boundary Conditions

2021 ◽  
pp. 291-314
Author(s):  
Luca Lorenzi ◽  
Abdelaziz Rhandi ◽  
Luca Lorenzi ◽  
Abdelaziz Rhandi
Keyword(s):  
Boundary Conditions ◽  
Elliptic Equations ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Homogeneous Dirichlet Boundary Conditions

Multiple Solutions for Perturbed Elliptic Equations in Unbounded Domains

2003 ◽  
Vol 3 (1) ◽  
pp. 1-23 ◽  
Author(s):  
A. Salvatore
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Perturbation Method ◽  
Elliptic Equations ◽  
Multiple Solutions ◽  
Schrodinger Equation ◽  
Dirichlet Boundary ◽  
Unbounded Domains ◽  
Dirichlet Boundary Conditions

AbstractWe look for solutions of a nonlinear perturbed Schrödinger equation with nonhomogeneous Dirichlet boundary conditions. By using a perturbation method introduced by Bolle, we prove the existence of multiple solutions in spite of the lack of the symmetry of the problem.

A Lane–Emden system with singular data

2011 ◽  
Vol 141 (6) ◽  
pp. 1279-1294 ◽  
Author(s):  
Marius Ghergu
Keyword(s):  
Boundary Conditions ◽  
Elliptic System ◽  
Bounded Domain ◽  
Existence And Uniqueness ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Homogeneous Dirichlet Boundary Conditions ◽  
Singular Data

We study the elliptic system −Δu = δ(x)−avp in Ω, −Δv = δ(x)−buq in Ω, subject to homogeneous Dirichlet boundary conditions. Here, Ω ⊂ ℝN, N ≥ 1, is a smooth and bounded domain, δ(x) = dist(x, ∂Ω), a, b ≥ 0 and p, q ∈ ℝ satisfy pq > −1. The existence, non-existence and uniqueness of solutions are investigated in terms of a, b, p and q.

Nonlinear Dirichlet problem with non local regional diffusion

2016 ◽  
Vol 19 (2) ◽  
Author(s):  
César E. Torres Ledesma
Keyword(s):  
Dirichlet Problem ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Nonlinear Term ◽  
Existence Of Solutions ◽  
Dirichlet Boundary Conditions ◽  
Nonlinear Dirichlet Problem ◽  
Non Local ◽  
Homogeneous Dirichlet Boundary Conditions

AbstractThe purpose of this paper is to study the existence of solutions for equations driven by a non-local regional operator with homogeneous Dirichlet boundary conditions. More precisely, we consider the problemwhere the nonlinear term

LEAST ENERGY NODAL SOLUTIONS OF THE BREZIS–NIRENBERG PROBLEM IN DIMENSION N = 5

2009 ◽  
Vol 11 (01) ◽  
pp. 59-69 ◽  
Author(s):  
PAOLO ROSELLI ◽  
MICHEL WILLEM
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
First Eigenvalue ◽  
Nodal Solutions ◽  
The First Eigenvalue ◽  
Homogeneous Dirichlet Boundary Conditions ◽  
Sign Changing Solutions ◽  
Nirenberg Problem ◽  
Least Energy

We prove the existence of (a pair of) least energy sign changing solutions of [Formula: see text] when Ω is a bounded domain in ℝN, N = 5 and λ is slightly smaller than λ1, the first eigenvalue of -Δ with homogeneous Dirichlet boundary conditions on Ω.

scholarly journals Existence and uniqueness of solution for Cahn-Hilliard hyperbolic phase field system with Dirichlet boundary conditions and polynomial potential

2018 ◽  
Vol 7 (1) ◽  
pp. 10
Author(s):  
A. J. Bissouesse ◽  
Daniel Moukoko ◽  
Franck Langa ◽  
Macaire Batchi
Keyword(s):  
Boundary Conditions ◽  
Phase Field ◽  
Dirichlet Boundary ◽  
Initial Conditions ◽  
Dirichlet Boundary Conditions ◽  
Uniqueness Of Solution ◽  
Polynomial Potential ◽  
Field System ◽  
Phase Field System ◽  
Homogeneous Dirichlet Boundary Conditions

Our aim in this article is to study the existence and the uniqueness of solution for Cahn-Hilliard hyperbolic phase-field system, with initial conditions, homogeneous Dirichlet boundary conditions, polynomial potential in a bounded and smooth domain.

scholarly journals Reaction-advection-diffusion competition models under lethal boundary conditions

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Kwangjoong Kim ◽  
Wonhyung Choi ◽  
Inkyung Ahn
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Eigenvalue Problems ◽  
Reaction Diffusion ◽  
Steady States ◽  
Dirichlet Boundary Conditions ◽  
Hostile Environment ◽  
Directed Movement ◽  
Constant Rate ◽  
Homogeneous Dirichlet Boundary Conditions

<p style='text-indent:20px;'>In this study, we consider a Lotka–Volterra reaction–diffusion–advection model for two competing species under homogeneous Dirichlet boundary conditions, describing a hostile environment at the boundary. In particular, we deal with the case in which one species diffuses at a constant rate, whereas the other species has a constant rate diffusion rate with a directed movement toward a better habitat in a heterogeneous environment with a lethal boundary. By analyzing linearized eigenvalue problems from the system, we conclude that the species dispersion in the advection direction is not always beneficial, and survival may be determined by the convexity of the environment. Further, we obtain the coexistence of steady-states to the system under the instability conditions of two semi-trivial solutions and the uniqueness of the coexistence steady states, implying the global asymptotic stability of the positive steady-state.</p>

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