Remarks on Ricceri’s variational principle and applications to the -Laplacian equations

2007 ◽  
Vol 67 (11) ◽  
pp. 3064-3075 ◽  
Author(s):  
Xianling Fan ◽  
Shao-Gao Deng
Keyword(s):  
Variational Principle ◽  
Laplacian Equations

Small perturbations of elliptic problems with variable growth in RN

2021 ◽  
Vol 477 (2249) ◽  
Author(s):  
Bin Ge ◽  
Hai-Cheng Liu ◽  
Bei-Lei Zhang
Keyword(s):  
Variational Principle ◽  
Mountain Pass Theorem ◽  
Elliptic Problems ◽  
Ekeland’S Variational Principle ◽  
Mountain Pass ◽  
Ekeland's Variational Principle ◽  
Small Perturbations ◽  
Whole Space ◽  
Laplacian Equations

In this paper, we study the existence of at least two non-trivial solutions for a class of p ( x )-Laplacian equations with perturbation in the whole space. Using Ekeland’s variational principle and the mountain pass theorem, under appropriate assumptions, we prove the existence of two solutions for the equations.

scholarly journals General solutions in Chern-Simons gravity and $$ T\overline{T} $$-deformations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Eva Llabrés
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Spin Connection ◽  
Departure Point ◽  
Boundary Stress ◽  
Chern Simons

Abstract We find the most general solution to Chern-Simons AdS3 gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection. We define a variational principle for Dirichlet boundary conditions and find the boundary stress tensor in the Chern-Simons formalism. Using this variational principle as the departure point, we show how to treat other choices of boundary conditions in this formalism, such as, including the mixed boundary conditions corresponding to a $$ T\overline{T} $$ T T ¯ -deformation.

On a strong minimum condition of a fractal variational principle

2021 ◽  
pp. 107199
Author(s):  
Ji-Huan He ◽  
Na Qie ◽  
Chun-hui He ◽  
Tareq Saeed
Keyword(s):  
Variational Principle ◽  
Minimum Condition

ALMOST ADDITIVE THERMODYNAMIC FORMALISM: SOME RECENT DEVELOPMENTS

2010 ◽  
Vol 22 (10) ◽  
pp. 1147-1179 ◽  
Author(s):  
LUIS BARREIRA
Keyword(s):  
Variational Principle ◽  
Existence And Uniqueness ◽  
Gibbs Measures ◽  
Thermodynamic Formalism ◽  
Topological Pressure ◽  
Present Stage ◽  
The Past ◽  
Recent Developments ◽  
General Sequences ◽  
Uniqueness Of Equilibrium

This is a survey on recent developments concerning a thermodynamic formalism for almost additive sequences of functions. While the nonadditive thermodynamic formalism applies to much more general sequences, at the present stage of the theory there are no general results concerning, for example, a variational principle for the topological pressure or the existence of equilibrium or Gibbs measures (at least without further restrictive assumptions). On the other hand, in the case of almost additive sequences, it is possible to establish a variational principle and to discuss the existence and uniqueness of equilibrium and Gibbs measures, among several other results. After presenting in a self-contained manner the foundations of the theory, the survey includes the description of three applications of the almost additive thermodynamic formalism: a multifractal analysis of Lyapunov exponents for a class of nonconformal repellers; a conditional variational principle for limits of almost additive sequences; and the study of dimension spectra that consider simultaneously limits into the future and into the past.

Sign in / Sign up

Export Citation Format

Share Document