On a Class of Infinite Semipositone Nonlinear Systems with Multiple Parameters
DOI:
https://doi.org/10.18311/jims/2017/6110Keywords:
Positive Solutions, Infinite Semipositone Systems, Sub-Super SolutionsAbstract
We analyze the existence of positive solutions of infinite semipositone nonlinear systems with multiple parameters of the form
{Δu = α1 (f (v)) - 1/un) + β1(h (u) - 1/un), x € Ω),-Δv = α2 (g (u)) - 1/vθ) + β2(k (v) - 1/uθ), x € Ω),
u = v = 0, x € δΩ),
where Ω is a bounded smooth domain of RN, η, θ ε (0, 1), and α1, α2, β1 and β2 are nonnegative parameters. Here f, g, h, k ε C ([0, ∞ ]), are non-decreasing functions and f(0), g(0), h(0), k(0) > 0. We use the method of sub-super solutions to prove the existence of positive solution for α1 + β1 and α2 + β2 large.
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Copyright (c) 2017 S. H. Rasouli
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2016-08-22
Published 2017-01-02
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