scholarly journals Foliation of an Asymptotically Flat End by Critical Capacitors

2022 ◽  
Vol 32 (2) ◽  
Author(s):  
Mouhammed Moustapha Fall ◽  
Ignace Aristide Minlend ◽  
Jesse Ratzkin
Keyword(s):  
Riemannian Manifold ◽  
Boundary Value Problem ◽  
Potential Theory ◽  
Critical Points ◽  
Boundary Value ◽  
Beltrami Operator ◽  
Neumann Operator ◽  
Asymptotically Flat ◽  
Dirichlet To Neumann Operator ◽  
Nonlocal Nature

AbstractWe construct a foliation of an asymptotically flat end of a Riemannian manifold by hypersurfaces which are critical points of a natural functional arising in potential theory. These hypersurfaces are perturbations of large coordinate spheres, and they admit solutions of a certain over-determined boundary value problem involving the Laplace–Beltrami operator. In a key step we must invert the Dirichlet-to-Neumann operator, highlighting the nonlocal nature of our problem.

scholarly journals On a class of non-local discrete boundary value problem

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Anass Ourraoui ◽  
Abdesslem Ayoujil
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Critical Points ◽  
Boundary Value ◽  
Discrete Problem ◽  
Three Solutions ◽  
Content Type ◽  
Three Critical Points Theorem ◽  
Discrete Boundary Value Problem ◽  
Non Local

PurposeIn this article, the authors discuss the existence and multiplicity of solutions for an anisotropic discrete boundary value problem in T-dimensional Hilbert space. The approach is based on variational methods especially on the three critical points theorem established by B. Ricceri.Design/methodology/approachThe approach is based on variational methods especially on the three critical points theorem established by B. Ricceri.FindingsThe authors study the existence of results for a discrete problem, with two boundary conditions type. Accurately, the authors have proved the existence of at least three solutions.Originality/valueAn other feature is that problem is with non-local term, which makes some difficulties in the proof of our results.

On the diffraction of an electromagnetic pulse by a wedge

1952 ◽  
Vol 212 (1111) ◽  
pp. 547-551 ◽  
Keyword(s):  
Plane Wave ◽  
Boundary Value Problem ◽  
Potential Theory ◽  
Electromagnetic Pulse ◽  
Boundary Value ◽  
Electromagnetic Disturbance ◽  
Two Dimensional ◽  
Arbitrary Polarization ◽  
Transient Electromagnetic ◽  
Classical Means

The diffraction by a conducting wedge of a transient electromagnetic disturbance in the form of a plane wave discontinuity having arbitrary polarization and direction of propagation is reduced to a pair of two-dimensional scalar problems. The solution to one of these is identical with that previously obtained for the analogous acoustical problem, while the second is attacked in a similar manner, using a Tschplygin transformation to reduce the boundary value problem to one in potential theory, which is then solved by classical means.

scholarly journals On the relation between interior critical points of positive solutions and parameters for a class of nonlinear boundary value problems

2002 ◽  
Vol 31 (12) ◽  
pp. 751-760
Author(s):  
G. A. Afrouzi ◽  
M. Khaleghy Moghaddam
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Critical Points ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Nonnegative Solutions ◽  
Nonlinear Boundary Value

We consider the boundary value problem−u″(x)=λf(u(x)),x∈(0,1);u′(0)=0;u′(1)+αu(1)=0, whereα>0,λ>0are parameters andf∈c2[0,∞)such thatf(0)<0. In this paper, we study for the two casesρ=0andρ=θ(ρis the value of the solution atx=0andθis such thatF(θ)=0whereF(s)=∫0sf(t)dt) the relation betweenλand the number of interior critical points of the nonnegative solutions of the above system.

Stability and constant boundary-value problems of harmonic maps with potential

2000 ◽  
Vol 68 (2) ◽  
pp. 145-154 ◽  
Author(s):  
Qun Chen
Keyword(s):  
Riemannian Manifold ◽  
Energy Density ◽  
Boundary Value Problem ◽  
Riemannian Manifolds ◽  
General Class ◽  
Harmonic Maps ◽  
Harmonic Map ◽  
Boundary Value ◽  
The Stability ◽  
Harmonic Maps With Potential

AbstractLet M, N be Riemannian manifolds, f: M → N a harmonic map with potential H, namely, a smooth critical point of the functional EH(f) = ∫M[e(f)−H(f)], where e(f) is the energy density of f. Some results concerning the stability of these maps between spheres and any Riemannian manifold are given. For a general class of M, this paper also gives a result on the constant boundary-value problem which generalizes the result of Karcher-Wood even in the case of the usual harmonic maps. It can also be applied to the static Landau-Lifshitz equations.

scholarly journals SOME MULTIPLICITY RESULTS TO THE EXISTENCE OF THREE SOLUTIONS FOR A DIRICHLET BOUNDARY VALUE PROBLEM INVOLVING THE P-LAPLACIAN

2011 ◽  
Vol 16 (3) ◽  
pp. 390-400 ◽  
Author(s):  
Shapour Heidarkhani ◽  
Ghasem Alizadeh Afrouzi
Keyword(s):  
Boundary Value Problem ◽  
Critical Points ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Main Tool ◽  
Dirichlet Boundary Value Problem ◽  
Positive Real ◽  
Three Solutions ◽  
Multiplicity Results ◽  
Uniformly Bounded

In this paper we prove the existence of two intervals of positive real parameters λ for a Dirichlet boundary value problem involving the p-Laplacian which admit three weak solutions, whose norms are uniformly bounded with respect to λ belonging to one of the two intervals. Our main tool is a three critical points theorem due to G. Bonanno [A critical points theorem and nonlinear differential problems, J. Global Optim., 28:249–258, 2004].

scholarly journals Existence of Three Solutions for a Nonlinear Fractional Boundary Value Problem via a Critical Points Theorem

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Chuanzhi Bai
Keyword(s):  
Boundary Value Problem ◽  
Critical Points ◽  
Boundary Value ◽  
Real Parameter ◽  
Fractional Boundary Value Problem ◽  
Positive Real ◽  
Three Solutions ◽  
Positive Real Parameter

This paper is concerned with the existence of three solutions to a nonlinear fractional boundary value problem as follows:(d/dt)((1/2)0Dtα-1(0CDtαu(t))-(1/2)tDTα-1(tCDTαu(t)))+λa(t)f(u(t))=0, a.e.  t∈[0,T],u(0)=u(T)=0,whereα∈(1/2,1], andλis a positive real parameter. The approach is based on a critical-points theorem established by G. Bonanno.

scholarly journals Positive Solutions for a Class of Discrete Mixed Boundary Value Problems with the p,q-Laplacian Operator

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Cuiping Li ◽  
Zhan Zhou
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Critical Points ◽  
Existence Of Solutions ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Mixed Boundary Value Problems

In this paper, we consider the existence of solutions for the discrete mixed boundary value problems involving p,q-Laplacian operator. By using critical points theory, we obtain the existence of at least two positive solutions for the boundary value problem under appropriate assumptions on the nonlinearity.

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