Qualitative properties of some bounded positive solutions to scalar field equations

2001 ◽  
Vol 13 (2) ◽  
pp. 191-211 ◽  
Author(s):  
Jérôme Busca ◽  
Patricio Felmer
Keyword(s):  
Scalar Field ◽  
Positive Solutions ◽  
Qualitative Properties ◽  
Field Equations ◽  
Scalar Field Equations

Min-Max Solutions to Some Scalar Field Equations

2012 ◽  
Vol 12 (1) ◽  
Author(s):  
Giuseppe Devillanova ◽  
Sergio Solimini
Keyword(s):  
Scalar Field ◽  
Positive Solutions ◽  
Multiplicity Result ◽  
Field Equations ◽  
Variational Structure ◽  
Scalar Field Equations

AbstractWe show the variational structure of a multiplicity result of positive solutions u ∈ H

Infinitely Many Positive Solutions to Some Scalar Field Equations with Nonsymmetric Coefficients

2012 ◽  
Vol 66 (3) ◽  
pp. 372-413 ◽  
Author(s):  
Giovanna Cerami ◽  
Donato Passaseo ◽  
Sergio Solimini
Keyword(s):  
Scalar Field ◽  
Positive Solutions ◽  
Field Equations ◽  
Scalar Field Equations

scholarly journals Quantum corrections to slow-roll inflation: scalar and tensor modes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Jens O. Andersen ◽  
Magdalena Eriksson ◽  
Anders Tranberg
Keyword(s):  
Scalar Field ◽  
Quantum Corrections ◽  
Tree Level ◽  
Field Equations ◽  
Slow Roll ◽  
Scalar Field Equations ◽  
Slow Rolling ◽  
Different Sources ◽  
Suitable Potential ◽  
Quadratic Order

Abstract Inflation is often described through the dynamics of a scalar field, slow-rolling in a suitable potential. Ultimately, this inflaton must be identified with the expectation value of a quantum field, evolving in a quantum effective potential. The shape of this potential is determined by the underlying tree-level potential, dressed by quantum corrections from the scalar field itself and the metric perturbations. Following [1], we compute the effective scalar field equations and the corrected Friedmann equations to quadratic order in both scalar field, scalar metric and tensor perturbations. We identify the quantum corrections from different sources at leading order in slow-roll, and estimate their magnitude in benchmark models of inflation. We comment on the implications of non-minimal coupling to gravity in this context.

scholarly journals COLLAPSING SCALAR FIELD WITH KINEMATIC SELF-SIMILARITY OF THE SECOND KIND IN (2+1) GRAVITY

2005 ◽  
Vol 14 (06) ◽  
pp. 1049-1061 ◽  
Author(s):  
R. CHAN ◽  
M. F. A. DA SILVA ◽  
J. F. VILLAS DA ROCHA ◽  
ANZHONG WANG
Keyword(s):  
Black Holes ◽  
Scalar Field ◽  
Gravitational Collapse ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Field Equations ◽  
Self Similarity ◽  
Global Properties ◽  
Scalar Field Equations

All the (2+1)-dimensional circularly symmetric solutions with kinematic self-similarity of the second kind to the Einstein-massless-scalar field equations are found and their local and global properties are studied. It is found that some of them represent gravitational collapse of a massless scalar field, in which black holes are always formed.

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