Ground states for nonlinear Kirchhoff equations with critical growth

2012 ◽  
Vol 193 (2) ◽  
pp. 473-500 ◽  
Author(s):  
Xiaoming He ◽  
Wenming Zou
Keyword(s):  
Ground States ◽  
Critical Growth ◽  
Kirchhoff Equations

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.

scholarly journals Ground states of nonlinear fractional Choquard equations with Hardy-Littlewood-Sobolev critical growth

2020 ◽  
Vol 19 (1) ◽  
pp. 123-144
Author(s):  
Hua Jin ◽  
◽  
Wenbin Liu ◽  
Huixing Zhang ◽  
Jianjun Zhang ◽  
...  
Keyword(s):  
Ground States ◽  
Critical Growth

scholarly journals Ground states for Kirchhoff-type equations with critical growth

2018 ◽  
Vol 17 (6) ◽  
pp. 2623-2638 ◽  
Author(s):  
Quanqing Li ◽  
◽  
Kaimin Teng ◽  
Xian Wu ◽  
◽  
...  
Keyword(s):  
Ground States ◽  
Critical Growth ◽  
Kirchhoff Type

Stationary Kirchhoff equations involving critical growth and vanishing potential

2020 ◽  
Vol 26 ◽  
pp. 74
Author(s):  
João Marcos do Ó ◽  
Marco Souto ◽  
Pedro Ubilla
Keyword(s):  
Positive Solutions ◽  
A Priori ◽  
A Priori Estimate ◽  
Critical Growth ◽  
Sobolev Embedding ◽  
Priori Estimate ◽  
Kirchhoff Equations ◽  
Kirchhoff Type ◽  
Local Case ◽  
Existence Of Positive Solutions

We establish the existence of positive solutions for a class of stationary Kirchhoff-type equations defined in the whole ℝ3 involving critical growth in the sense of the Sobolev embedding and potentials, which may decay to zero at infinity. We use minimax techniques combined with an appropriate truncated argument and a priori estimate. These results are new even for the local case, which corresponds to nonlinear Schrödinger equations.

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