Eigenfunction Expansion Method for Multiple Solutions of Semilinear Elliptic Equations with Polynomial Nonlinearity

2013 ◽  
Vol 51 (5) ◽  
pp. 2680-2699 ◽  
Author(s):  
Xuping Zhang ◽  
Jintao Zhang ◽  
Bo Yu
Keyword(s):  
Elliptic Equations ◽  
Eigenfunction Expansion ◽  
Multiple Solutions ◽  
Expansion Method ◽  
Semilinear Elliptic Equations ◽  
Eigenfunction Expansion Method ◽  
Semilinear Elliptic ◽  
Polynomial Nonlinearity

Multiple solutions for some semilinear elliptic equations

1987 ◽  
Vol 276 (4) ◽  
pp. 643-656 ◽  
Author(s):  
Vittorio Cafagna ◽  
Gabriella Tarantello
Keyword(s):  
Elliptic Equations ◽  
Multiple Solutions ◽  
Semilinear Elliptic Equations ◽  
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.

Multiple solutions for semilinear elliptic equations in unbounded cylinder domains

2004 ◽  
Vol 134 (4) ◽  
pp. 719-731 ◽  
Author(s):  
Tsing-San Hsu
Keyword(s):  
Dirichlet Problem ◽  
Positive Solution ◽  
Elliptic Equations ◽  
Multiple Solutions ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic ◽  
Unbounded Cylinder ◽  
Image Position

In this paper, we show that if b(x) ≥ b∞ > 0 in Ω̄ and there exist positive constants C, δ, R0 such that where x = (y, z) ∈ RN with y ∈ Rm, z ∈ Rn, N = m + n ≥ 3, m ≥ 2, n ≥ 1, 1 < p < (N + 2)/(N − 2), ω ⊆ Rm a bounded C1,1 domain and Ω = ω × Rn, then the Dirichlet problem −Δu + u = b(x)|u|p−1u in Ω has a solution that changes sign in Ω, in addition to a positive solution.

Sign in / Sign up

Export Citation Format

Share Document