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Volume 12, Issue 1
On the Existence and Stability of Positive Solutions for Some Pairs of Differential Equations

Zongming Guo

J. Part. Diff. Eq., 12 (1999), pp. 41-54.

Published online: 1999-12

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  • Abstract
In this paper, we are concerned with the existence and stability of the positive solutions of a semilinear elliptic system - Δu(x) = a(x)v^6(x) + e(x) - Δv(x) = b(x}u^μ(x) + m(x) \qquad in Ω u = v = 0 \qquad\qquad on ∂Ω where Ω ⊂ R^N is a bounded domain with smooth boundary ∂Ω. It is shown that under the suitable conditions on \delta, μ, there exist a stable and an unstable positive solutions for this system if e and m are sufficiently small in L^∞.
  • Keywords

Positive solutions multiple solutions stability semilincar differential systems

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@Article{JPDE-12-41, author = {}, title = {On the Existence and Stability of Positive Solutions for Some Pairs of Differential Equations}, journal = {Journal of Partial Differential Equations}, year = {1999}, volume = {12}, number = {1}, pages = {41--54}, abstract = { In this paper, we are concerned with the existence and stability of the positive solutions of a semilinear elliptic system - Δu(x) = a(x)v^6(x) + e(x) - Δv(x) = b(x}u^μ(x) + m(x) \qquad in Ω u = v = 0 \qquad\qquad on ∂Ω where Ω ⊂ R^N is a bounded domain with smooth boundary ∂Ω. It is shown that under the suitable conditions on \delta, μ, there exist a stable and an unstable positive solutions for this system if e and m are sufficiently small in L^∞.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5523.html} }
TY - JOUR T1 - On the Existence and Stability of Positive Solutions for Some Pairs of Differential Equations JO - Journal of Partial Differential Equations VL - 1 SP - 41 EP - 54 PY - 1999 DA - 1999/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5523.html KW - Positive solutions KW - multiple solutions KW - stability KW - semilincar differential systems AB - In this paper, we are concerned with the existence and stability of the positive solutions of a semilinear elliptic system - Δu(x) = a(x)v^6(x) + e(x) - Δv(x) = b(x}u^μ(x) + m(x) \qquad in Ω u = v = 0 \qquad\qquad on ∂Ω where Ω ⊂ R^N is a bounded domain with smooth boundary ∂Ω. It is shown that under the suitable conditions on \delta, μ, there exist a stable and an unstable positive solutions for this system if e and m are sufficiently small in L^∞.
Zongming Guo . (2019). On the Existence and Stability of Positive Solutions for Some Pairs of Differential Equations. Journal of Partial Differential Equations. 12 (1). 41-54. doi:
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