We deal with the problems of four boundary points conditions for both differential inclusions and differential equations with and without moving constraints. Using a very recent result we prove existence of generalized solutions for some differential inclusions and some differential equations with moving constraints. The results obtained improve the recent results obtained by Papageorgiou and Ibrahim-Gomaa. Also by means of a rather different approach based on an existence theorem due to O. N. Ricceri and B. Ricceri we prove existence results improving earlier theorems by Gupta and Marano.
We study the Dirichlet boundary value problem for the p-Laplacian of the form −∆pu − λ1|u| p−2u = f in Ω, u = 0 on ∂Ω, where Ω ⊂ N is a bounded domain with smooth boundary ∂Ω, N ≥ 1, p > 1, f ∈ C(Ω) and λ1 > 0 is the first eigenvalue of ∆p. We study the geometry of the energy functional Ep(u) = 1⁄ p ∫ Ω |∇u| p − λ1⁄ p ∫ Ω |u| p − ∫ Ω fu and show the difference between the case 1 <p< 2 and the case p > 2. We also give the characterization of the right hand sides f for which the above Dirichlet problem is solvable and has multiple solutions.
The paper considers a fuzzification of the notion of quantaloid of K. I. Rosenthal, which replaces enrichment in the category of ⋁-semilattices with that in the category of modules over a given unital commutative quantale. The resulting structures are called quantale algebroids. We show that their constitute a monadic category and prove a representation theorem for them using the notion of nucleus adjusted for our needs. We also characterize the lattice of nuclei on a free quantale algebroid. At the end of the paper, we prove that the category of quantale algebroids has a monoidal structure given by tensor product.
The fuzzification of (normal) $B$-subalgebras is considered, and some related properties are investigated. A characterization of a fuzzy $B$-algebra is given.
In this paper the concept of fuzzy nearly C-compactness is introduced in fuzzy topological spaces and fuzzy bitopological spaces. Several characterizations and some interesting properties of these spaces are discussed. The properties of fuzzy almost continuous and fuzzy almost open functions are also discussed.
The simultaneous occurrence of conditional independences among subvectors of a regular Gaussian vector is examined. All configurations of the conditional independences within four jointly regular Gaussian variables are found and completely characterized in terms of implications involving conditional independence statements. The statements induced by the separation in any simple graph are shown to correspond to such a configuration within a regular Gaussian vector.
We discuss how the choice of the functional setting and the definition of the weak solution affect the existence and uniqueness of the solution to the equation −∆pu = f in Ω, where Ω is a very general domain in RN , including the case Ω = RN .
Some generalizations of the Ostrowski inequality, the Milovanović-Pečarić-Fink inequality, the Dragomir-Agarwal inequality and the Hadamard inequality are given.
An S-closed submodule of a module M is a submodule N for which M/N is nonsingular. A module M is called a generalized CS-module (or briefly, GCS-module) if any S-closed submodule N of M is a direct summand of M. Any homomorphic image of a GCS-module is also a GCS-module. Any direct sum of a singular (uniform) module and a semi-simple module is a GCS-module. All nonsingular right R-modules are projective if and only if all right R-modules are GCS-modules., Qingyi Zeng., and Obsahuje seznam literatury