Positive solutions and spectral properties of weakly coupled elliptic systems
β Scribed by W Allegretto
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 394 KB
- Volume
- 120
- Category
- Article
- ISSN
- 0022-247X
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π SIMILAR VOLUMES
## Abstract The paper deals with the existence, multiplicity and nonexistence of positive radial solutions for the elliptic system div(|β|^__p__ β2^β) + __Ξ»k~i~__ (|__x__ |) __f^i^__ (__u__~1~, β¦,__u~n~__) = 0, __p__ > 1, __R__~1~ < |__x__ | < __R__~2~, __u~i~__ (__x__) = 0, on |__x__ | = __R__~1~
We show that entire positive solutions exist for the semilinear elliptic system u = p x v Ξ± , v = q x u Ξ² on R N , N β₯ 3, for positive Ξ± and Ξ², provided that the nonnegative functions p and q are continuous and satisfy appropriate decay conditions at infinity. We also show that entire solutions fail
Let M u, Β¨s 0, N u, Β¨s 0 define two distinct phase curves β« , β« in the 1 2 Ε½ . u,Β¨-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 β¬ u q uM u, Β¨s 0, β¬Β¨q Β¨N u, Β¨s 0 in β;R n Ε½ . Ε½