scholarly journals Asymptotic behavior of least energy solutions to a semilinear Dirichlet problem near the critical exponent

1998 ◽  
Vol 50 (1) ◽  
pp. 139-153 ◽  
Author(s):  
Juncheng WEI
Keyword(s):  
Asymptotic Behavior ◽  
Dirichlet Problem ◽  
Critical 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].

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