Non-existence and Uniqueness Results for Boundary Value Problems for Yang-mills Connections
نویسنده
چکیده
We show uniqueness results for the Dirichlet problem for YangMills connections defined in n-dimensional (n ≥ 4) star-shaped domains with flat boundary values. This result also shows the non-existence result for the Dirichlet problem in dimension 4, since in 4-dimension, there exist countably many connected components of connections with prescribed Dirichlet boundary value. We also show non-existence results for the Neumann problem. Examples of non-minimal Yang-Mills connections for the Dirichlet and the Neumann problems are also given.
منابع مشابه
Existence of positive solution to a class of boundary value problems of fractional differential equations
This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Than...
متن کاملExistence and uniqueness of solutions for p-laplacian fractional order boundary value problems
In this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-Laplacian fractional order differential equations. We use Schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. We include some examples to show the applicability of our results.
متن کاملSolutions for some non-linear fractional differential equations with boundary value problems
In recent years, X.J.Xu [1] has been proved some results on mixed monotone operators. Following the paper of X.J.Xu, we study the existence and uniqueness of the positive solutions for non-linear differential equations with boundary value problems.
متن کاملExistence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem
In this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form $D_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0
متن کاملExiststence and uniqueness of positive solution for a class of boundary value problem including fractional differential equation
In this paper we investigate a kind of boundary value problem involving a fractional differential equation. We study the existence of positive solutions of the problem that fractional derivative is the Reimann-Liouville fractional derivative. At first the green function is computed then it is proved that the green function is positive. We present necessary and sufficient conditions for existen...
متن کامل