scholarly journals Asymptotic behavior of least energy solutions for a 2D nonlinear Neumann problem with large exponent

2014 ◽  
Vol 411 (1) ◽  
pp. 95-106 ◽  
Author(s):  
Futoshi Takahashi
Keyword(s):  
Asymptotic Behavior ◽  
Neumann Problem ◽  
Nonlinear Neumann Problem ◽  
Large Exponent ◽  
Least Energy Solutions ◽  
Least Energy

Least energy solutions for indefinite biharmonic problems via modified Nehari–Pankov manifold

2018 ◽  
Vol 20 (04) ◽  
pp. 1750047 ◽  
Author(s):  
Miaomiao Niu ◽  
Zhongwei Tang ◽  
Lushun Wang
Keyword(s):  
Asymptotic Behavior ◽  
Potential Function ◽  
Biharmonic Equation ◽  
Positive Function ◽  
Energy Solution ◽  
Zero Set ◽  
Least Energy Solution ◽  
Least Energy Solutions ◽  
Least Energy ◽  
Biharmonic Problems

In this paper, by using a modified Nehari–Pankov manifold, we prove the existence and the asymptotic behavior of least energy solutions for the following indefinite biharmonic equation: [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text] is a parameter, [Formula: see text] is a nonnegative potential function with nonempty zero set [Formula: see text], [Formula: see text] is a positive function such that the operator [Formula: see text] is indefinite and non-degenerate for [Formula: see text] large. We show that both in subcritical and critical cases, equation [Formula: see text] admits a least energy solution which for [Formula: see text] large localized near the zero set [Formula: see text].

Sign in / Sign up

Export Citation Format

Share Document