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 a previous paper, the author considered several conditions for effective zero-dimensionality of a computable metric space X; each of the (classically equivalent) properties of having vanishing small or large inductive dimension, or covering dimension, or having a countable basis of clopen sets, can be interpreted as multi-valued operations, and the computability of these operations was shown...

Sequence converges is an important research object in topology and analysis, since it closely related to continuity, compactness other properties. In this article, we use the notion of regularly convergence, which a generalization convergence notion, define sequentially closed sets operator sequential closure; then consider thier charactarizations prove that are coincide regular spaces. Finally...

in this paper, we study some properties of the near sr-compactnessin l-topological spaces, where l is a fuzzy lattice. the near sr-compactness isa kind of compactness between lowen’s fuzzy compactness and sr-compactness,and it preserves desirable properties of compactness in general topologicalspaces.

Abstract The paper introduces a broad family of metrics applicable to finite and countably infinite strings, or, by extension, formal structures serving as semantics for countable languages. main focus is on applications sets pointed Kripke models, modal logics. For the resulting metric spaces, classifies topological properties including which are topologically equivalent, providing sufficient ...

In this paper, we study some properties of the near SR-compactnessin L-topological spaces, where L is a fuzzy lattice. The near SR-compactness isa kind of compactness between Lowen’s fuzzy compactness and SR-compactness,and it preserves desirable properties of compactness in general topologicalspaces.

We establish the existence of a nontrivial solution to systems of coupled Poisson equations with critical growth in unbounded domains. The proofs rely on a generalized linking theorem due to Krysewski and Szulkin [9], and on a concentration-compactness argument since the Palais-Smale condition fails at all critical levels. Mathematical Subject Classification. 35J50, 35J55

De Finetti would claim that we can make sense of a draw in which each positive integer has equal probability of winning. This requires a uniform probability distribution over the natural numbers, violating countable additivity. Countable additivity thus appears not to be a fundamental constraint on subjective probability. It does, however, seem mandated by Dutch Book arguments similar to those ...

This work is devoted to the study of certain cardinality modifications of paracompactness and compactness in the setting of linearly ordered spaces. Some of the concepts treated here have previously been studied by Aquaro [l]1, Gulden [4], Kennison [5], Mansfield [6], Morita [7], and Poppe [9]. On the other hand, the concept of m-boundedness, introduced in §2, is new. Our main results (Theorems...