Regular convergence, together with other types of have been studied since the 1970s for discrete approximations linear operators. In this paper, we consider eigenvalue approximation a compact operator $T$ that can be written as an problem holomorphic Fredholm function $F(\eta) = T-\frac{1}{\eta} I$. Focusing on finite element methods (conforming, discontinuous Galerkin, non-conforming, etc.), s...

Abstract. In this paper, we define the notion of C*-affine maps in the unital *-rings and we investigate the C*-extreme points of the graph and epigraph of such maps. We show that for a C*-convex map f on a unital *-ring R satisfying the positive square root axiom with an additional condition, the graph of f is a C*-face of the epigraph of f. Moreover, we prove som...

In this paper, we study the existence of multiple solutions to a class of p-biharmonic elliptic equations, pu – pu + V(x)|u|p–2u = λh1(x)|u|m–2u + h2(x)|u|q–2u, x ∈RN , where 1 0. By variational methods, we obtain the existence of infini...

The behavior of solutions to the biharmonic equation is well-understood in smooth domains. In the past two decades substantial progress has also been made for the polyhedral domains and domains with Lipschitz boundaries. However, very little is known about higher order elliptic equations in the general setting. In this paper we introduce new integral identities that allow to investigate the sol...

We construct biharmonic real hypersurfaces and Lagrangian submanifolds of Clifford torus type in CPn via the Hopf fibration; and get new examples of biharmonic submanifolds in S as byproducts .

Let R be a Riemannian manifold without a biharmonic Green function defined on it and Ω a domain in R. A necessary and sufficient condition is given for the existence of a biharmonic Green function on Ω.