On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value
Articles
G. A. Afrouzi
Mazandaran University, Iran
S. H. Rasouli
Mazandaran University, Iran
Published 2006-11-01
https://doi.org/10.15388/NA.2006.11.4.14736
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Keywords

positive solutions
sub-super solution

How to Cite

Afrouzi, G.A. and Rasouli, S.H. (2006) “On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value”, Nonlinear Analysis: Modelling and Control, 11(4), pp. 323–329. doi:10.15388/NA.2006.11.4.14736.

Abstract

This study concerns the existence of positive solutions to classes of boundary value problems of the form
−∆u = g(x,u), x ∈ Ω,
u(x) = 0, x ∈ ∂Ω,
where ∆ denote the Laplacian operator, Ω is a smooth bounded domain in RN (N ≥ 2) with ∂Ω of class C2, and connected, and g(x, 0) < 0 for some x ∈ Ω (semipositone problems). By using the method of sub-super solutions we prove the existence of positive solution to special types of g(x,u).

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