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The Relationships Between Equilibria and Positive Solutions of Certain Nonlinear Elliptic Systems

✍ Scribed by Lige Li; Guoxiang Cao; Yaping Liu

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
344 KB
Volume
209
Category
Article
ISSN
0022-247X

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✦ Synopsis

Let M u, ¨s 0, N u, ¨s 0 define two distinct phase curves ⌫ , ⌫ in the 1 2 Ž . u,¨-phase plane. This paper presents results on the relationships among the positive equilibria, the phase curves, and the existence of positive solutions to the PDE system ⌬ u q uM u, ¨s 0, ⌬¨q ¨N u, ¨s 0 in ⍀;R n Ž . Ž .

under Dirichlet boundary conditions, where ⍀ is a bounded domain and M, N are monotone functions.

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✍ Donal O'Regan; Haiyan Wang 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 178 KB

## Abstract The paper deals with the existence, multiplicity and nonexistence of positive radial solutions for the elliptic system div(|∇|^__p__ –2^∇) + __λk~i~__ (|__x__ |) __f^i^__ (__u__~1~, …,__u~n~__) = 0, __p__ > 1, __R__~1~ < |__x__ | < __R__~2~, __u~i~__ (__x__) = 0, on |__x__ | = __R__~1~