In this paper we study the solvability of backward doubly stochastic differential equations (BDSDEs for short) with polynomial growth coefficients and their connections with SPDEs. The corresponding SPDE is in a very general form, which may depend on the derivative of the solution. We use Wiener-Sobolev compactness arguments to derive a strongly convergent subsequence of approximating SPDEs. Fo...

In this article, we prove the theorem concerning existence of solutions for some nonlinear integral equations. As an application, investigate problem Fredholm equations using technique relative compactness in conjunction with fixed point theorem. Our are placed space functions satisfying Hölder condition. work is more general than previous works [1-3]. last section, show efficiency approach on ...

We are concerned with the global weak continuity of Cartan structural system—or equivalently, Gauss–Codazzi–Ricci system—on semi-Riemannian manifolds lower regularity. For this purpose, we first formulate and prove a geometric compensated compactness theorem on vector bundles over regularity (Theorem 3.2), extending classical quadratic compactness. then deduce $$L^p$$ system for $$p>2$$ : famil...

In [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba- nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case,...

We prove new multiplicity results for the Brézis-Nirenberg problem p -Laplacian. Our proofs are based on a abstract critical point theorem involving Z 2 -cohomological index that requires less compactness than ( PS ) condition.

Abstract Lindström’s theorem obviously fails as a characterization of first-order logic without identity ( $\mathcal {L}_{\omega \omega }^{-} $ ). In this note, we provide fix: show that is maximal abstract satisfying weak form the isomorphism property (suitable for identity-free languages and studied in [11]), Löwenheim–Skolem property, compactness. Furthermore, compactness can be replaced by ...

We formulate a restricted version of the Tukey-Teichmüller Theorem that we denote by (rTT). We then prove that (rTT) and (BPI) are equivalent in ZF and that (rTT) applies rather naturally to several equivalent forms of (BPI): Alexander Subbase Theorem, Stone Representation Theorem, Model Existence and Compactness Theorems for propositional and first-order logic. We also give two variations of (...