Existence of the Minimal Positive Solution of Some Nonlinear Elliptic Systems When the Nonlinearity is the Sum of a Sublinear and a Superlinear Term

Nicolae Tarfulea

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Nicolae Tarfulea. Existence of the Minimal Positive Solution of Some Nonlinear Elliptic Systems When the Nonlinearity is the Sum of a Sublinear and a Superlinear Term[J]. Applied Mathematics and Mechanics, 2000, 21(3): 253-259.

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Existence of the Minimal Positive Solution of Some Nonlinear Elliptic Systems When the Nonlinearity is the Sum of a Sublinear and a Superlinear Term

Nicolae Tarfulea

Department of Mathematics, the Pennsylvania State University, University Park, PA 16902, U S A

Received Date: 1999-03-01
Publish Date: 2000-03-15

Abstract

Abstract

It is shown that there exists Λ>0 such that, for every λ∈(0,Λ), the semilinear elliptic system:-$u=λu|u|^q-1+u|u|^p-1-vinΩ, -$v=δu-γvin Ω,u=v=0 onΩ,where Ω∈R^N>(N≥2) is a bounded domain with smooth boundary and 0<q<1<p,has a minimal positive solution (u_λ,v_λ). Moreover:u_λ and v_λ are strictly increasing with respect to λ.
- reaction diffusion system,
- positive solution,
- nonlinear equation

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References(9)

References

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