scholarly journals Positive multipeak solutions to a zero mass problem in exterior domains

2019 ◽  
pp. 1950062
Author(s):  
Mónica Clapp ◽  
Liliane A. Maia ◽  
Benedetta Pellacci
Keyword(s):  
Field Equation ◽  
Scalar Field ◽  
Mass Formula ◽  
Exterior Domains ◽  
Mass Problem ◽  
Zero Mass ◽  
Scalar Field Equation ◽  
Nonlinear Scalar Field

We establish the existence of positive multipeak solutions to the nonlinear scalar field equation with zero mass [Formula: see text] where [Formula: see text] with [Formula: see text], [Formula: see text], and the nonlinearity [Formula: see text] is subcritical at infinity and supercritical near the origin. We show that the number of positive multipeak solutions becomes arbitrarily large as [Formula: see text].

scholarly journals Existence of a Positive Solution to a Nonlinear Scalar Field Equation with Zero Mass at Infinity

2018 ◽  
Vol 18 (4) ◽  
pp. 745-762 ◽  
Author(s):  
Mónica Clapp ◽  
Liliane A. Maia
Keyword(s):  
Field Equation ◽  
Scalar Field ◽  
Positive Solution ◽  
Ground State ◽  
Bound State ◽  
Zero Mass ◽  
Scalar Field Equation ◽  
Nonlinear Scalar Field ◽  
Decay Assumption

AbstractWe establish the existence of a positive solution to the problem-\Delta u+V(x)u=f(u),\quad u\in D^{1,2}(\mathbb{R}^{N}),for {N\geq 3}, when the nonlinearity f is subcritical at infinity and supercritical near the origin, and the potential V vanishes at infinity. Our result includes situations in which the problem does not have a ground state. Then, under a suitable decay assumption on the potential, we show that the problem has a positive bound state.

scholarly journals Zero mass case for a fractional Berestycki–Lions-type problem

2018 ◽  
Vol 7 (3) ◽  
pp. 365-374 ◽  
Author(s):  
Vincenzo Ambrosio
Keyword(s):  
Field Equation ◽  
Scalar Field ◽  
Variational Methods ◽  
Positive Solution ◽  
Fractional Laplacian ◽  
Spherically Symmetric ◽  
Type Problem ◽  
Zero Mass ◽  
Scalar Field Equation ◽  
Mass Case

AbstractIn this work we study the following fractional scalar field equation:\left\{\begin{aligned} \displaystyle(-\Delta)^{s}u&\displaystyle=g^{\prime}(u)% \quad\mbox{in }\mathbb{R}^{N},\\ \displaystyle u&\displaystyle>0,\end{aligned}\right.where {N\geq 2}, {s\in(0,1)}, {(-\Delta)^{s}} is the fractional Laplacian and the nonlinearity {g\in C^{2}(\mathbb{R})} is such that {g^{\prime\prime}(0)=0}. By using variational methods, we prove the existence of a positive solution which is spherically symmetric and decreasing in {r=|x|}.

scholarly journals Nonlinear scalar field equation with competing nonlocal terms *

Nonlinearity ◽  
2021 ◽  
Vol 34 (8) ◽  
pp. 5687-5707
Author(s):  
Pietro d’Avenia ◽  
Jarosław Mederski ◽  
Alessio Pomponio
Keyword(s):  
Field Equation ◽  
Scalar Field ◽  
Scalar Field Equation ◽  
Nonlinear Scalar Field ◽  
Nonlocal Terms

scholarly journals THE REAL SCALAR FIELD EQUATION FOR NARIAI BLACK HOLE IN THE 5D SCHWARZSCHILD–DE SITTER BLACK STRING SPACE

2007 ◽  
Vol 22 (24) ◽  
pp. 4451-4465 ◽  
Author(s):  
MOLIN LIU ◽  
HONGYA LIU ◽  
CHUNXIAO WANG ◽  
YONGLI PING
Keyword(s):  
Black Hole ◽  
Field Equation ◽  
Scalar Field ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
De Sitter ◽  
Black String ◽  
Transmission Coefficients ◽  
Scalar Field Equation ◽  
Continuous Potential

The Nariai black hole, whose two horizons are lying close to each other, is an extreme and important case in the research of black hole. In this paper we study the evolution of a massless scalar field scattered around in 5D Schwarzschild–de Sitter black string space. Using the method shown by Brevik and Simonsen (2001) we solve the scalar field equation as a boundary value problem, where real boundary condition is employed. Then with convenient replacement of the 5D continuous potential by square barrier, the reflection and transmission coefficients (R, T) are obtained. At last, we also compare the coefficients with the usual 4D counterpart.

scholarly journals Scalar field equation in the presence of signature change

1993 ◽  
Vol 48 (6) ◽  
pp. 2587-2590 ◽  
Author(s):  
Tevian Dray ◽  
Corinne A. Manogue ◽  
Robin W. Tucker
Keyword(s):  
Field Equation ◽  
Scalar Field ◽  
Scalar Field Equation ◽  
Signature Change
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