scholarly journals Robin and Neumann problems for a class of singularly perturbed semilinear elliptic equations

1979 ◽  
Vol 34 (1) ◽  
pp. 55-73 ◽  
Author(s):  
F.A Howes
Keyword(s):  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Singularly Perturbed ◽  
Neumann Problems ◽  
Semilinear Elliptic

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.

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.

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