An existence result on positive solutions for a class of p-Laplacian systems

• DOI: 10.1016/j.na.2003.10.024
• Publication Date: 2004-01-16T10:15:36Z
• Authors: D.D. Hai; R. Shivaji
• Keywords: 0101 mathematics; 01 natural sciences

Abstract Consider the system −Δ p u=λf(v) in Ω, −Δ p v=λg(u) in Ω, u=v=0 on ∂Ω, where Δpz=div(|∇z|p−2∇z),p>1, λ is a positive parameter, and Ω is a bounded domain in RN with smooth boundary ∂Ω . We prove the existence of a large positive solution for λ large when lim x→∞ f(M(g(x) 1/(p−1) ) x p−1 =0 for every M>0. In particular, we do not assume any sign conditions on f(0) or g(0).