The context of much of the work in this paper is that of a backward-shift invariant subspace of the form KB :1⁄4 HðDÞ~BHðDÞ; where B is some infinite Blaschke product. We address (but do not fully answer) the question: For which B can one find a (convergent) sequence f fngn1⁄41 in KB such that the sequence of real measures flog j fnjdyg N n1⁄41 converges weak-star to some nontrivial singular me...

Existence and multiplicity results are obtained for superlinear p-Laplacian equations without the Ambrosetti and Rabinowitz condition. To overcome the difficulty that the Palais-Smale sequences of the EulerLagrange functional may be unbounded, we consider the Cerami sequences. Our results extend the recent results of Miyagaki and Souto [ J. Differential Equations 245 (2008), 3628–3638].

In this paper we obtain the interior C regularity of the quasilinear elliptic equations of divergence form. Our basic tools are the elementary local L estimates and weak Harnack inequality for second-order linear elliptic equations, and the compactness method.

A weak concept of compactness for nonmonotonic logics is proposed, which is suitable for several nonmonotonic logics, for which Makinsons smallest cumulative extension as well as Freund/Lehmanns canonical extension fail.

Let X be a locally compact Hausdorff topological space, let V = ( v n , k ) ∈ N $\mathcal {V}=(v_{n,k})_{n,k\in {\mathbb {N}}}$ system of positive continuous functions on and φ self-map X. The composition operators C : f ↦ ∘ $C_\varphi f\mapsto \ f\,\circ\, \varphi$ the weighted function (LF)-spaces {V}C(X)$ 0 {V}_0C(X)$ resp.) (PLB)-spaces A {A}C(X)$ {A}_0C(X)$ are studied. We characterize whe...

We prove a balancing condition for weak limits of families of embedded minimal surfaces of finite total curvature. We use it to prove compactness theorems for certain families of minimal surfaces. Mathematics Subject Classification (2000). Primary 53A10.

We present a proof of Sklar’s Theorem that uses topological arguments, namely compactness (under the weak topology) of the class of copulas and some density properties of the class of distribution functions.