In this paper we establish some results of existence of infinitely many solutions for an elliptic equation involving the p-biharmonic and the p-Laplacian operators coupled with Navier boundary ...conditions where the nonlinearities depend on two real parameters and do not satisfy any symmetric condition. The nature of the approach is variational and the main tool is an abstract result of Ricceri. The novelty in the application of this abstract tool is the use of a class of test functions which makes the assumptions on the data easier to verify.
This paper contains some results of existence of infinitely many solutions to an elliptic equation involving the p(x)-biharmonic operator coupled with Navier boundary conditions where the ...nonlinearities depend on two real parameters and do not possess any symmetric property. The approach is variational and the main tool is an abstract result of Ricceri.
We examine the semilinear resonant problem
−
Δ
u
=
λ
1
u
+
λ
g
(
u
)
in
Ω
,
u
≥
0
in
Ω
,
u
|
∂
Ω
=
0
,
where
Ω
⊂
R
N
is a smooth, bounded domain,
λ
1
is the first eigenvalue of
−
Δ
in
Ω
,
λ
>
...0
. Inspired by a previous result in literature involving power-type nonlinearities, we consider here a generic sublinear term
g
and single out conditions to ensure: the existence of solutions for all
λ
>
0
; the validity of the strong maximum principle for sufficiently small
λ
. The proof rests upon variational arguments.
Monotone weak Lindelöfness Bonanzinga, Maddalena; Cammaroto, Filippo; Pansera, Bruno A.
Central European journal of mathematics,
06/2011, Letnik:
9, Številka:
3
Journal Article
Recenzirano
Odprti dostop
The definition of monotone weak Lindelöfness is similar to monotone versions of other covering properties:
X
is monotonically weakly Lindelöf if there is an operator
r
that assigns to every open ...cover
U
a family of open sets
r
(
U
) so that (1) ∪
r
(
U
) is dense in
X
, (2)
r
(
U
) refines
U
, and (3)
r
(
U
) refines
r
(
V
) whenever
U
refines
V
. Some examples and counterexamples of monotonically weakly Lindelöf spaces are given and some basic properties such as the behavior with respect to products and subspaces are discussed.
In this article, we extend the work on minimal Hausdorff functions initiated by Cammaroto, Fedorchuk and Porter in a 1998 paper. Also, minimal Urysohn functions are introduced and developed. The ...properties of heredity and productivity are examined and developed for both minimal Hausdorff and minimal Urysohn functions.
Remarks on monotone (weak) Lindelöfness Bonanzinga, Maddalena; Cammaroto, Filippo; Sakai, Masami
Topology and its applications,
07/2017, Letnik:
225
Journal Article
Recenzirano
Odprti dostop
Using Erdös–Rado's theorem, we show that (1) every monotonically weakly Lindelöf space satisfies the property that every family of cardinality c+ consisting of nonempty open subsets has an ...uncountable linked subfamily; (2) every monotonically Lindelöf space has strong caliber (c+,ω1), in particular a monotonically Lindelöf space is hereditarily c-Lindelöf and hereditarily c-separable. (1) gives an answer of a question posed in Bonanzinga, Cammaroto and Pansera 3, and (2) gives partial answers of questions posed in Levy and Matveev 15. Some other properties on monotonically (weakly) Lindelöf spaces are also discussed. For example, we show that the Pixley–Roy space PR(X) of a space X is monotonically Lindelöf if and only if X is countable and every finite power of X is monotonically Lindelöf.
On the cardinality of Hausdorff spaces Cammaroto, Filippo; Catalioto, Andrei; Porter, Jack
Topology and its applications,
01/2013, Letnik:
160, Številka:
1
Journal Article
Recenzirano
Odprti dostop
A common generalization for two of the main streams of cardinality inequalities is developed; each stream derives from the famous inequality established by A.V. Arhangelʼskiĭ in 1969 for Hausdorff ...spaces. At the end of one stream is the recent inequality by Bella and at the end of the second stream is the 1988 inequality by Bella and Cammaroto. This generalization is extended and used to analyze a result containing an increasing chain of spaces that satisfies the same cardinality inequality. The paper is concluded with some open problems.
Diagonalizations of dense families Bonanzinga, Maddalena; Cammaroto, Filippo; Pansera, Bruno Antonio ...
Topology and its applications,
03/2014, Letnik:
165
Journal Article
Recenzirano
Odprti dostop
We develop a unified framework for the study of classic and new properties involving diagonalizations of dense families in topological spaces. We provide complete classification of these properties. ...Our classification draws upon a large number of methods and constructions scattered in the literature, and on several novel results concerning the classic properties.
Projective versions of selection principles Bonanzinga, Maddalena; Cammaroto, Filippo; Matveev, Mikhail
Topology and its applications,
04/2010, Letnik:
157, Številka:
5
Journal Article
Recenzirano
Odprti dostop
All spaces are assumed to be Tychonoff. A space
X is called projectively
P
(where
P
is a topological property) if every continuous second countable image of
X is
P
. Characterizations of projectively ...Menger spaces
X in terms of continuous mappings
f
:
X
→
R
ω
, of Menger base property with respect to separable pseudometrics and a selection principle restricted to countable covers by cozero sets are given. If all finite powers of
X are projectively Menger, then all countable subspaces of
C
p
(
X
)
have countable fan tightness. The class of projectively Menger spaces contains all Menger spaces as well as all
σ-pseudocompact spaces, and all spaces of cardinality less than
d
. Projective versions of Hurewicz, Rothberger and other selection principles satisfy properties similar to the properties of projectively Menger spaces, as well as some specific properties. Thus,
X is projectively Hurewicz iff
C
p
(
X
)
has the Monotonic Sequence Selection Property in the sense of Scheepers;
βX is Rothberger iff
X is pseudocompact and projectively Rothberger. Embeddability of the countable fan space
V
ω
into
C
p
(
X
)
or
C
p
(
X
,
2
)
is characterized in terms of projective properties of
X.
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