On equivalent norms for fractional spaces

1969 ◽  
pp. 257-280 ◽  
Author(s):  
K. K. Golovkin
Keyword(s):  
Equivalent Norms ◽  
Fractional Spaces

scholarly journals Equivalent norms in polynomial spaces and applications

2017 ◽  
Vol 445 (2) ◽  
pp. 1200-1220 ◽  
Author(s):  
Gustavo Araújo ◽  
P. Jiménez-Rodríguez ◽  
Gustavo A. Muñoz-Fernández ◽  
Juan B. Seoane-Sepúlveda
Keyword(s):  
Equivalent Norms

scholarly journals Periodic solutions for a fractional asymptotically linear problem

2018 ◽  
Vol 149 (03) ◽  
pp. 593-615
Author(s):  
Vincenzo Ambrosio ◽  
Giovanni Molica Bisci
Keyword(s):  
Neumann Boundary ◽  
Index Theory ◽  
Careful Analysis ◽  
Asymptotically Linear ◽  
Existence And Multiplicity ◽  
Degenerate Elliptic ◽  
Subcritical Nonlinearity ◽  
Fractional Spaces ◽  
Non Local ◽  
Asymptotically Linear Problem

We study the existence and multiplicity of periodic weak solutions for a non-local equation involving an odd subcritical nonlinearity which is asymptotically linear at infinity. We investigate such problem by applying the pseudo-index theory developed by Bartolo, Benci and Fortunato [11] after transforming the problem to a degenerate elliptic problem in a half-cylinder with a Neumann boundary condition, via a Caffarelli-Silvestre type extension in periodic setting. The periodic nonlocal case, considered here, presents, respect to the cases studied in the literature, some new additional difficulties and a careful analysis of the fractional spaces involved is necessary.

scholarly journals Momentum transforms and Laplacians in fractional spaces

2012 ◽  
Vol 16 (4) ◽  
pp. 1315-1348 ◽  
Author(s):  
Gianluca Calcagni ◽  
Giuseppe Nardelli
Keyword(s):  
Fractional Spaces

scholarly journals Equivalent norms on analytic subspaces of LP

1987 ◽  
Vol 126 (1) ◽  
pp. 238-249 ◽  
Author(s):  
John P. Nolan ◽  
Zachariah Sinkala
Keyword(s):  
Equivalent Norms

Equivalent norms on Banach Jordan algebras

1979 ◽  
Vol 86 (2) ◽  
pp. 261-270 ◽  
Author(s):  
M. A. Youngson
Keyword(s):  
Jordan Algebra ◽  
Sufficient Conditions ◽  
Equivalent Norm ◽  
Jordan Algebras ◽  
The Self ◽  
Equivalent Norms ◽  
Positive Elements ◽  
Definition Of ◽  
Necessary And Sufficient

1. Introduction. Recently Kaplansky suggested the definition of a suitable Jordan analogue of B*-algebras, which we call J B*-algebras (see (10) and (11)). In this article, we give a characterization of those complex unital Banach Jordan algebras which are J B*-algebras in an equivalent norm. This is done by generalizing results of Bonsall ((3) and (4)) to give necessary and sufficient conditions on a real unital Banach Jordan algebra under which it is the self-adjoint part of a J B*-algebra in an equivalent norm. As a corollary we also obtain a characterization of the cones in a Banach Jordan algebra which are the set of positive elements of a J B*-algebra.

scholarly journals Sign-Changing Solutions for a Class of Zero Mass Nonlocal Schrödinger Equations

2019 ◽  
Vol 19 (1) ◽  
pp. 113-132 ◽  
Author(s):  
Vincenzo Ambrosio ◽  
Giovany M. Figueiredo ◽  
Teresa Isernia ◽  
Giovanni Molica Bisci
Keyword(s):  
Careful Analysis ◽  
Continuous Functions ◽  
Nehari Manifold ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Deformation Lemma ◽  
Fractional Schrödinger Equations ◽  
Fractional Spaces ◽  
The Nehari Manifold ◽  
Sign Changing Solutions

Abstract We consider the following class of fractional Schrödinger equations: (-\Delta)^{\alpha}u+V(x)u=K(x)f(u)\quad\text{in }\mathbb{R}^{N}, where {\alpha\in(0,1)} , {N>2\alpha} , {(-\Delta)^{\alpha}} is the fractional Laplacian, V and K are positive continuous functions which vanish at infinity, and f is a continuous function. By using a minimization argument and a quantitative deformation lemma, we obtain the existence of a sign-changing solution. Furthermore, when f is odd, we prove that the above problem admits infinitely many nontrivial solutions. Our result extends to the fractional framework some well-known theorems proved for elliptic equations in the classical setting. With respect to these cases studied in the literature, the nonlocal one considered here presents some additional difficulties, such as the lack of decompositions involving positive and negative parts, and the non-differentiability of the Nehari Manifold, so that a careful analysis of the fractional spaces involved is necessary.

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