Sufficient and necessary conditions for ground state sign-changing solutions to the Schrödinger-Poisson system with cubic nonlinearity on bounded domains

2021 ◽  
pp. 107570
Author(s):  
Shubin Yu ◽  
Ziheng Zhang
Keyword(s):  
Ground State ◽  
Necessary Conditions ◽  
Bounded Domains ◽  
Poisson System ◽  
Cubic Nonlinearity ◽  
Sufficient And Necessary Conditions ◽  
Sign Changing Solutions

Compactness of embeddings of function spaces on quasi-bounded domains and the distribution of eigenvalues of related elliptic operators

2013 ◽  
Vol 56 (3) ◽  
pp. 829-851 ◽  
Author(s):  
Hans-Gerd Leopold ◽  
Leszek Skrzypczak
Keyword(s):  
Asymptotic Behaviour ◽  
Spectral Properties ◽  
Necessary Conditions ◽  
Function Spaces ◽  
Elliptic Operators ◽  
Bounded Domains ◽  
Entropy Numbers ◽  
Sobolev Embeddings ◽  
Distribution Of Eigenvalues ◽  
Sufficient And Necessary Conditions

AbstractWe prove sufficient and necessary conditions for compactness of the Sobolev embeddings of Besov and Triebel–Lizorkin spaces defined on bounded and unbounded uniformly E-porous domains. The asymptotic behaviour of the corresponding entropy numbers is calculated. Some applications to the spectral properties of elliptic operators are described.

Sign in / Sign up

Export Citation Format

Share Document