scholarly journals Componentwise localization of critical points for functionals defined on product spaces

2021 ◽  
pp. 1-27
Author(s):  
Radu Precup
Keyword(s):  
Critical Points ◽  
Cartesian Product ◽  
Mountain Pass ◽  
Product Spaces ◽  
Minimax Points

A new notion of linking is introduced to treat minima as minimax points in a unitary way. Critical points are located in conical annuli making possible to obtain multiplicity. For functionals defined on a Cartesian product, the localization of critical points is given on components and the variational properties of the components can differ, part of them being of minimum type, others of mountain pass type.

Haar polynomials on Cartesian product spaces

1969 ◽  
Vol 36 (1) ◽  
pp. 193-205 ◽  
Author(s):  
M. S. Grosof ◽  
D. J. Newman
Keyword(s):  
Cartesian Product ◽  
Product Spaces

scholarly journals Solitary waves for nonlinear Klein–Gordon–Maxwell and Schrödinger–Maxwell equations

2004 ◽  
Vol 134 (5) ◽  
pp. 893-906 ◽  
Author(s):  
Teresa D'Aprile ◽  
Dimitri Mugnai
Keyword(s):  
Solitary Waves ◽  
Critical Points ◽  
Variational Approach ◽  
Maxwell Equations ◽  
Energy Functional ◽  
Nonlinear Schrödinger Equations ◽  
Mountain Pass ◽  
Schrödinger Equations ◽  
Nonlinear Schrodinger Equations ◽  
Klein Gordon

In this paper we study the existence of radially symmetric solitary waves for nonlinear Klein–Gordon equations and nonlinear Schrödinger equations coupled with Maxwell equations. The method relies on a variational approach and the solutions are obtained as mountain-pass critical points for the associated energy functional.

scholarly journals On Extremal Set Partitions in Cartesian Product Spaces

1993 ◽  
Vol 2 (3) ◽  
pp. 211-220 ◽  
Author(s):  
Rudolf Ahlswede ◽  
Ning Cai
Keyword(s):  
Cartesian Product ◽  
Product Spaces ◽  
Minimal Size ◽  
Set Partitions ◽  
Partition Number ◽  
Vertex Set ◽  
Extremal Set

The partition number of a product hypergraph is introduced as the minimal size of a partition of its vertex set into sets that are edges. This number is shown to be multiplicative if all factors are graphs with all loops included.

scholarly journals A generalization of Lucas' theorem to vector spaces

1993 ◽  
Vol 16 (2) ◽  
pp. 267-276 ◽  
Author(s):  
Neyamat Zaheer
Keyword(s):  
Critical Points ◽  
Vector Spaces ◽  
Inner Product ◽  
Product Spaces ◽  
Linear Combinations ◽  
Inner Product Spaces ◽  
Complex Valued ◽  
Vector Valued

The classical Lucas' theorem on critical points of complex-valued polynomials has been generalized (cf. [1]) to vector-valued polynomials defined onK-inner product spaces. In the present paper, we obtain a generalization of Lucas' theorem to vector-valued abstract polynomials defined on vector spaces, in general, which includes the above result of the author [1] inK-inner product spaces. Our main theorem also deduces a well-known result due to Marden on linear combinations of polynomial and its derivative. At the end, we discuss some examples in support of certain claims.

scholarly journals Inequalities for Hypo-q-Norms on a Cartesian Product of Inner Product Spaces

2017 ◽  
Author(s):  
Silvestru Dragomir
Keyword(s):  
Cartesian Product ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
Inner Products ◽  
Reverse Inequalities

In this paper we introduce the hypo-q-norms on a Cartesian product of inner product spaces. A representation of these norms in terms of inner products, the equivalence with the q-norms on a Cartesian product and some reverse inequalities obtained via the scalar Shisha-Mond, Birnacki et al., Grüss type inequalities, Boas-Bellman and Bombieri type inequalities are also given.

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