Uniqueness and existence of positive solutions for some semilinear elliptic systems

2004 ◽  
Vol 59 (6) ◽  
pp. 993-999 ◽  
Author(s):  
Masaaki Maniwa
Keyword(s):  
Positive Solutions ◽  
Elliptic Systems ◽  
Semilinear Elliptic Systems ◽  
Semilinear Elliptic ◽  
Existence Of Positive Solutions ◽  
Uniqueness And Existence

scholarly journals Positive solutions for semilinear elliptic systems with sign-changing potentials

2016 ◽  
Vol 24 (1) ◽  
pp. 383-390
Author(s):  
Noureddine Zeddini ◽  
Adel Ben Dkhil
Keyword(s):  
Fixed Point ◽  
Dirichlet Problem ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Elliptic Systems ◽  
Semilinear Elliptic Systems ◽  
Semilinear Elliptic ◽  
Existence Of Positive Solutions ◽  
Compact Boundary

AbstractIn this paper, we study the existence of positive solutions of the Dirichlet problem -Δu = λ p(x)f(u; v) ; -Δv = λ q(x)g(u; v); in D, and u = v = 0 on ∂∞D, where D ⊂ Rn (n ≥ 3) is an C1,1-domain with compact boundary and λ > 0. The potential functions p; q are not necessarily bounded, may change sign and the functions f; g : ℝ2→ ℝ are continuous with f(0; 0) > 0, g(0; 0) > 0. By applying the Leray- Schauder fixed point theorem, we establish the existence of positive solutions for λ sufficiently small.

Sign in / Sign up

Export Citation Format

Share Document