scholarly journals A note on multiplicity of solutions near resonance of semilinear elliptic equations

2019 ◽  
Vol 18 (6) ◽  
pp. 3351-3365
Author(s):  
Jinlong Bai ◽  
◽  
Desheng Li ◽  
Chunqiu Li ◽  
Keyword(s):  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Multiplicity Of Solutions ◽  
Semilinear Elliptic ◽  
Near Resonance

scholarly journals Multiplicity of Solutions for Neumann Problems for Semilinear Elliptic Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Yu-Cheng An ◽  
Hong-Min Suo
Keyword(s):  
Critical Point ◽  
Critical Point Theory ◽  
Elliptic Equations ◽  
Point Theory ◽  
Semilinear Elliptic Equations ◽  
Multiplicity Of Solutions ◽  
Neumann Problems ◽  
Minimax Methods ◽  
Semilinear Elliptic ◽  
Near Resonance

Using the minimax methods in critical point theory, we study the multiplicity of solutions for a class of Neumann problems in the case near resonance. The results improve and generalize some of the corresponding existing results.

scholarly journals Multiple solutions for singularly perturbed semilinear elliptic equations in bounded domains

2005 ◽  
Vol 2005 (2) ◽  
pp. 185-205
Author(s):  
Michinori Ishiwata
Keyword(s):  
Elliptic Equations ◽  
Multiple Solutions ◽  
Point Of View ◽  
Semilinear Elliptic Equations ◽  
Singularly Perturbed ◽  
Bounded Domains ◽  
Three Solutions ◽  
Multiplicity Of Solutions ◽  
Semilinear Elliptic ◽  
The Relationship

We are concerned with the multiplicity of solutions of the following singularly perturbed semilinear elliptic equations in bounded domainsΩ:−ε2Δu+a(⋅)u=u|u|p−2inΩ,u>0inΩ,u=0on∂Ω. The main purpose of this paper is to discuss the relationship between the multiplicity of solutions and the profile ofa(⋅)from the variational point of view. It is shown that ifahas a “peak” inΩ, then (P) has at least three solutions for sufficiently smallε.

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