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On a Class of Infinite Semipositone Nonlinear Systems with Multiple Parameters


Affiliations
  • Babol Noshirvani University of Technology, Department of Mathematics, Babol, Iran, Islamic Republic of
     

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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.


Keywords

Positive Solutions, Infinite Semipositone Systems, Sub-Super Solutions.
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  • On a Class of Infinite Semipositone Nonlinear Systems with Multiple Parameters

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Authors

S. H. Rasouli
, Iran, Islamic Republic of

Abstract


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.


Keywords


Positive Solutions, Infinite Semipositone Systems, Sub-Super Solutions.

References