TY - JOUR

T1 - Global preservation of nodal structure in coupled systems of nonlinear sturm-liouville boundary value problems

AU - Cantrell, Robert Stephen

N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 1989/11

Y1 - 1989/11

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).

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U2 - 10.1090/S0002-9939-1989-0975633-X

DO - 10.1090/S0002-9939-1989-0975633-X

M3 - Article

AN - SCOPUS:84966247811

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 -