scholarly journals Existence and Multiplicity of Solutions of Semilinear Elliptic Equations

2001 ◽  
Vol 256 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Chun-Lei Tang ◽  
Xing-Ping Wu
Keyword(s):  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic

scholarly journals Positive Solutions for Elliptic Problems with the Nonlinearity Containing Singularity and Hardy-Sobolev Exponents

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yong-Yi Lan ◽  
Xian Hu ◽  
Bi-Yun Tang
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Elliptic Problems ◽  
Semilinear Elliptic Equations ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic ◽  
Multiplicity Of Positive Solutions

In this paper, we study multiplicity of positive solutions for a class of semilinear elliptic equations with the nonlinearity containing singularity and Hardy-Sobolev exponents. Using variational methods, we establish the existence and multiplicity of positive solutions for the problem.

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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