Abstract
In this paper, we examine the solution set to the coupled system where λ, μ∈ R, x∈ [a, b], and the system (*) is subject to zero Dirichlet boundary data on u and v. We determine conditions on f and g which permit us to assert the existence of continua of solutions to (*) characterized by u having n−1 simple zeros in (a, b), v having m− 1 simple zeros in (a, b), where n and m are positive but not necessarily equal integers. Moreover, we also determine conditions under which these continua link solutions to (*) of the form (λ,μ, u, 0) with u having n− 1 simple zeros in (a, b) to solutions of (*) of the form (λ,μ, 0, v) with v having m−1 simple zeros in (a, b).
| Original language | English (US) |
|---|---|
| Pages (from-to) | 633-644 |
| Number of pages | 12 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 107 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1989 |
Fingerprint
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
Global preservation of nodal structure in coupled systems of nonlinear sturm-liouville boundary value problems. / Cantrell, Robert.
In: Proceedings of the American Mathematical Society, Vol. 107, No. 3, 1989, p. 633-644.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Global preservation of nodal structure in coupled systems of nonlinear sturm-liouville boundary value problems
AU - Cantrell, Robert
PY - 1989
Y1 - 1989
N2 - In this paper, we examine the solution set to the coupled system where λ, μ∈ R, x∈ [a, b], and the system (*) is subject to zero Dirichlet boundary data on u and v. We determine conditions on f and g which permit us to assert the existence of continua of solutions to (*) characterized by u having n−1 simple zeros in (a, b), v having m− 1 simple zeros in (a, b), where n and m are positive but not necessarily equal integers. Moreover, we also determine conditions under which these continua link solutions to (*) of the form (λ,μ, u, 0) with u having n− 1 simple zeros in (a, b) to solutions of (*) of the form (λ,μ, 0, v) with v having m−1 simple zeros in (a, b).
AB - In this paper, we examine the solution set to the coupled system where λ, μ∈ R, x∈ [a, b], and the system (*) is subject to zero Dirichlet boundary data on u and v. We determine conditions on f and g which permit us to assert the existence of continua of solutions to (*) characterized by u having n−1 simple zeros in (a, b), v having m− 1 simple zeros in (a, b), where n and m are positive but not necessarily equal integers. Moreover, we also determine conditions under which these continua link solutions to (*) of the form (λ,μ, u, 0) with u having n− 1 simple zeros in (a, b) to solutions of (*) of the form (λ,μ, 0, v) with v having m−1 simple zeros in (a, b).
UR - http://www.scopus.com/inward/record.url?scp=84966247811&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84966247811&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-1989-0975633-X
DO - 10.1090/S0002-9939-1989-0975633-X
M3 - Article
VL - 107
SP - 633
EP - 644
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 3
ER -