We consider the existence of positive solutions for the system
-Δui = λ[fi(u1,u2,...,um) - hi]; Ω
ui = 0; ∂Ω
where λ > 0 is a parameter, Δ is the Laplacian operator, Ω is a bounded domain in Rn; n ≥ 1 with a smooth boundary ∂Ω, fi are C1 functions satisfying f1(0,0,...,0) = 0, lim z→∞ fi(z,z,...,z) = ∞ and lim z→∞ fi(z,z,...,z)/z = 0, and hi are nonnegative continuous functions in Ω for i = 1,2,...,m. In this paper for λ large we discuss the existence of a positive solution u := (u1,u2,...,um). We establish our results by using the method of sub-super solutions.
© 2000 Watam
Castro, A., C. Maya and R. Shivaji. “An existence result for a class of sublinear semipositone systems”, Dynamics of Continuous, Discrete and Impulsive Systems, Volume 7, Number 4 (2000), pp. 533-540.