scholarly journals Multiple positive radial solutions on annuli for nonlinear Neumann problems with large growth

2010 ◽  
Vol 18 (2) ◽  
pp. 217-235 ◽  
Author(s):  
Denis Bonheure ◽  
Enrico Serra
Keyword(s):  
Radial Solutions ◽  
Neumann Problems ◽  
Positive Radial Solutions ◽  
Large Growth ◽  
Nonlinear Neumann Problems

Coercive and noncoercive nonlinear Neumann problems with indefinite potential

2016 ◽  
Vol 28 (3) ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Vicenţiu D. Rădulescu
Keyword(s):  
Differential Operator ◽  
Neumann Problems ◽  
Nonhomogeneous Differential Operator ◽  
Indefinite Potential ◽  
Nonlinear Neumann Problems

AbstractWe consider nonlinear Neumann problems driven by a nonhomogeneous differential operator and an indefinite potential. In this paper we are concerned with two distinct cases. We first consider the case where the reaction is (

scholarly journals Weighted fourth order elliptic problems in the unit ball

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Zongming Guo ◽  
Fangshu Wan
Keyword(s):  
Asymptotic Behavior ◽  
Singular Point ◽  
Unit Ball ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Weighted Sobolev Spaces ◽  
Radial Solutions ◽  
Dirichlet Problems ◽  
Uniqueness Results ◽  
Positive Radial Solutions

<p style='text-indent:20px;'>Existence and uniqueness of positive radial solutions of some weighted fourth order elliptic Navier and Dirichlet problems in the unit ball <inline-formula><tex-math id="M1">\begin{document}$ B $\end{document}</tex-math></inline-formula> are studied. The weights can be singular at <inline-formula><tex-math id="M2">\begin{document}$ x = 0 \in B $\end{document}</tex-math></inline-formula>. Existence of positive radial solutions of the problems is obtained via variational methods in the weighted Sobolev spaces. To obtain the uniqueness results, we need to know exactly the asymptotic behavior of the solutions at the singular point <inline-formula><tex-math id="M3">\begin{document}$ x = 0 $\end{document}</tex-math></inline-formula>.</p>

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