Ground state solution of critical biharmonic equation with Hardy potential and p-Laplacian

2021 ◽  
Vol 112 ◽  
pp. 106802
Author(s):  
Yu Su ◽  
Hongxia Shi
Keyword(s):  
Ground State ◽  
Biharmonic Equation ◽  
Ground State Solution ◽  
State Solution ◽  
Hardy Potential

Ground state solution for the Schrödinger equation with Hardy potential and critical Sobolev exponent

2021 ◽  
pp. 1-19
Author(s):  
Jing Zhang ◽  
Lin Li
Keyword(s):  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Critical Sobolev Exponent ◽  
Ground State Solution ◽  
Nehari Manifold ◽  
State Solution ◽  
Hardy Potential ◽  
Asymptotically Periodic ◽  
Sobolev Exponent

In this paper, we consider the following Schrödinger equation (0.1) − Δ u − μ u | x | 2 + V ( x ) u = K ( x ) | u | 2 ∗ − 2 u + f ( x , u ) , x ∈ R N , u ∈ H 1 ( R N ) , where N ⩾ 4, 0 ⩽ μ < μ ‾, μ ‾ = ( N − 2 ) 2 4 , V is periodic in x, K and f are asymptotically periodic in x, we take advantage of the generalized Nehari manifold approach developed by Szulkin and Weth to look for the ground state solution of (0.1).

scholarly journals Nodal ground state solution to a biharmonic equation via dual method

2016 ◽  
Vol 260 (6) ◽  
pp. 5174-5201 ◽  
Author(s):  
Claudianor O. Alves ◽  
Alânnio B. Nóbrega
Keyword(s):  
Ground State ◽  
Biharmonic Equation ◽  
Ground State Solution ◽  
State Solution ◽  
Dual Method

Exact Ground State Solution for Anyons with spin-$\frac {1}{2}$

1992 ◽  
Vol 17 (1) ◽  
pp. 107-110
Author(s):  
Shun-Qing Shen ◽  
J. Cai ◽  
Rui-Bao Tao
Keyword(s):  
Ground State ◽  
Ground State Solution ◽  
State Solution ◽  
Exact Ground State
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