Characterization of ground states for an M‐coupled system in a bounded domain with critical exponent

2020 ◽  
Vol 43 (11) ◽  
pp. 6871-6887
Author(s):  
Qihan He ◽  
Jing Yang
Keyword(s):  
Critical Exponent ◽  
Bounded Domain ◽  
Ground States ◽  
Coupled System

scholarly journals Synthesis and characterization of [7]triangulene

Nanoscale ◽  
2021 ◽  
Author(s):  
Shantanu Mishra ◽  
Kun Xu ◽  
Kristjan Eimre ◽  
Hartmut Komber ◽  
Ji Ma ◽  
...  
Keyword(s):  
High Spin ◽  
Ground States ◽  
Synthesis And Characterization ◽  
Spintronic Devices

Triangulene and its π-extended homologues constitute non-Kekulé polyradical frameworks with high-spin ground states, and are anticipated to be key components of organic spintronic devices. We report a combined in-solution and...

Multiple solutions for a non-homogeneous elliptic equation at the critical exponent

2004 ◽  
Vol 134 (1) ◽  
pp. 69-87 ◽  
Author(s):  
Mónica Clapp ◽  
Manuel Del Pino ◽  
Monica Musso
Keyword(s):  
Elliptic Equation ◽  
Boundary Conditions ◽  
Critical Exponent ◽  
Bounded Domain ◽  
Multiple Solutions ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Sign Changing Solutions ◽  
Homogeneous Elliptic Equation

We consider the equation−Δu = |u|4/(N−2)u + εf(x) under zero Dirichlet boundary conditions in a bounded domain Ω in RN exhibiting certain symmetries, with f ≥ 0, f ≠ 0. In particular, we find that the number of sign-changing solutions goes to infinity for radially symmetric f, as ε → 0 if Ω is a ball. The same is true for the number of negative solutions if Ω is an annulus and the support of f is compact in Ω.

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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