Multiplicity and uniqueness of positive solutions for nonhomogeneous semilinear elliptic equation with critical exponent

2016 ◽  
Vol 32 (1) ◽  
pp. 81-94 ◽  
Author(s):  
Na Ba ◽  
Yan-yan Wang ◽  
Lie Zheng
Keyword(s):  
Elliptic Equation ◽  
Critical Exponent ◽  
Positive Solutions ◽  
Semilinear Elliptic Equation ◽  
Semilinear Elliptic

Multi-bump solutions of -Δn = K(x)u (n+2)/(n-2) on lattices in ℝ n

2018 ◽  
Vol 2018 (743) ◽  
pp. 163-211 ◽  
Author(s):  
Yanyan Li ◽  
Juncheng Wei ◽  
Haoyuan Xu
Keyword(s):  
Elliptic Equation ◽  
Critical Exponent ◽  
Critical Point ◽  
Semilinear Elliptic Equation ◽  
Natural Conditions ◽  
Semilinear Elliptic ◽  
Infinite Lattices

Abstract We consider the following semilinear elliptic equation with critical exponent: Δ u = K(x) u^{(n+2)/(n-2)} , u > 0 in \mathbb{R}^{n} , where {n\geq 3} , {K>0} is periodic in ( x_{1} ,…, x_{k} ) with 1 \leq k < (n-2)/2. Under some natural conditions on K near a critical point, we prove the existence of multi-bump solutions where the centers of bumps can be placed in some lattices in {\mathbb{R}^{k}} , including infinite lattices. We also show that for k \geq (n-2)/2, no such solutions exist.

Sign in / Sign up

Export Citation Format

Share Document