An Existence Result for a Class of Sublinear Semipositone Systems

Authors

Alfonso Castro, Harvey Mudd CollegeFollow
C. Maya, University of North Carolina at Greensboro
Ratnasingham Shivaji, Mississippi State University

Document Type

Article

Department

Mathematics (HMC)

Publication Date

2004

Abstract

We consider the existence of positive solutions for the system

-Δu_i = λ[f_i(u₁,u₂,...,u_m) - h_i]; Ω

u_i = 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, f_i are C¹ functions satisfying f₁(0,0,...,0) = 0, lim z→∞ f_i(z,z,...,z) = ∞ and lim z→∞ f_i(z,z,...,z)/z = 0, and h_i 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,...,u_m). We establish our results by using the method of sub-super solutions.

Comments

Archived with permission from Watam Press.

Rights Information

© 2000 Watam

Recommended Citation

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.