Positive and oscillatory radial solutions of semilinear elliptic equations

Shaohua Chen, William R. Derrick and Joseph A. Cima

International Journal of Stochastic Analysis, 1997, vol. 10, 1-14

Abstract:

We prove that the nonlinear partial differential equation Δ u + f ( u ) + g ( | x | , u ) = 0 , in ℝ n , n ≥ 3 , with u ( 0 ) > 0 , where f and g are continuous, f ( u ) > 0 and g ( | x | , u ) > 0 for u > 0 , and lim u → 0 + f ( u ) u q = B > 0 , for 1 < q < n / ( n − 2 ) , has no positive or eventually positive radial solutions. For g ( | x | , u ) ≡ 0 , when n / ( n − 2 ) ≤ q < ( n + 2 ) / ( n − 2 ) the same conclusion holds provided 2 F ( u ) ≥ ( 1 − 2 / n ) u f ( u ) , where F ( u ) = ∫ 0 u f ( s ) d s . We also discuss the behavior of the radial solutions for f ( u ) = u 3 + u 5 and f ( u ) = u 4 + u 5 in ℝ 3 when g ( | x | , u ) ≡ 0 .

Date: 1997
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJSA/10/823105.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJSA/10/823105.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:823105

DOI: 10.1155/S1048953397000105

Access Statistics for this article

More articles in International Journal of Stochastic Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().