scholarly journals Exact multiplicity of solutions and S-shaped bifurcation curve for a class of semilinear elliptic equations

2007 ◽  
Vol 331 (1) ◽  
pp. 263-278 ◽  
Author(s):  
Yuhua Zhao ◽  
Yuwen Wang ◽  
Junping Shi
2005 ◽  
Vol 2005 (2) ◽  
pp. 185-205
Author(s):  
Michinori Ishiwata

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.


2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Yu-Cheng An ◽  
Hong-Min Suo

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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