scholarly journals Qualitative properties of Hénon type equations with exponential nonlinearity

Nonlinearity ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 492-512
Author(s):  
Zongming Guo ◽  
Xia Huang ◽  
Dong Ye ◽  
Feng Zhou
Keyword(s):  
Radial Solutions ◽  
Qualitative Properties ◽  
Exponential Nonlinearity ◽  
Complete Answer ◽  
Qualitative Properties Of Solutions ◽  
Funct Anal ◽  
Precise Asymptotic ◽  
Asymptotic Behaviours

Abstract We are interested in the qualitative properties of solutions of the Hénon type equations with exponential nonlinearity. First, we classify the stable at infinity solutions of Δu + |x| α e u = 0 in R N , which gives a complete answer to the problem considered in Wang and Ye (2012 J. Funct. Anal. 262 1705–1727). Secondly, existence and precise asymptotic behaviours of entire radial solutions to Δ2 u = |x| α e u are obtained. Then we classify the stable and stable at infinity radial solutions to Δ2 u = |x| α e u in any dimension.

Qualitative properties of solutions to set optimization problems

2021 ◽  
Vol 40 (2) ◽  
Author(s):  
Lam Quoc Anh ◽  
Nguyen Huu Danh ◽  
Pham Thanh Duoc ◽  
Tran Ngoc Tam
Keyword(s):  
Optimization Problems ◽  
Set Optimization ◽  
Qualitative Properties ◽  
Qualitative Properties Of Solutions

Old and New Results for First Order Periodic ODEs without Uniqueness: a Comprehensive Study by Lower and Upper Solutions

2004 ◽  
Vol 4 (3) ◽  
Author(s):  
Franco Obersnel ◽  
Pierpaolo Omari
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Lower And Upper Solutions ◽  
Elementary Approach ◽  
Qualitative Properties ◽  
First Order ◽  
The Past ◽  
The Cauchy Problem ◽  
Qualitative Properties Of Solutions ◽  
Comprehensive Study

AbstractAn elementary approach, based on a systematic use of lower and upper solutions, is employed to detect the qualitative properties of solutions of first order scalar periodic ordinary differential equations. This study is carried out in the Carathéodory setting, avoiding any uniqueness assumption, in the future or in the past, for the Cauchy problem. Various classical and recent results are recovered and generalized.

scholarly journals Radially symmetric solutions to the Hénon–Lane–Emden system on the critical hyperbola

2014 ◽  
Vol 16 (03) ◽  
pp. 1350030 ◽  
Author(s):  
Roberta Musina ◽  
K. Sreenadh
Keyword(s):  
Variational Methods ◽  
Existence Results ◽  
Qualitative Properties ◽  
Radially Symmetric Solutions ◽  
Qualitative Properties Of Solutions

We use variational methods to study the existence of non-trivial and radially symmetric solutions to the Hénon–Lane–Emden system with weights, when the exponents involved lie on the "critical hyperbola". We also discuss qualitative properties of solutions and non-existence results.

scholarly journals Choquard-type equations with Hardy–Littlewood–Sobolev upper-critical growth

2018 ◽  
Vol 8 (1) ◽  
pp. 1184-1212 ◽  
Author(s):  
Daniele Cassani ◽  
Jianjun Zhang
Keyword(s):  
Variational Methods ◽  
Critical Exponent ◽  
Sobolev Inequality ◽  
Ground States ◽  
Critical Growth ◽  
Qualitative Behavior ◽  
Schrödinger Equations ◽  
Qualitative Properties ◽  
Concentration Phenomena ◽  
Qualitative Properties Of Solutions

Abstract We are concerned with the existence of ground states and qualitative properties of solutions for a class of nonlocal Schrödinger equations. We consider the case in which the nonlinearity exhibits critical growth in the sense of the Hardy–Littlewood–Sobolev inequality, in the range of the so-called upper-critical exponent. Qualitative behavior and concentration phenomena of solutions are also studied. Our approach turns out to be robust, as we do not require the nonlinearity to enjoy monotonicity nor Ambrosetti–Rabinowitz-type conditions, still using variational methods.

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