Annali di Matematica Pura ed Applicata

, Volume 120, Issue 1, pp 293–303 | Cite as

A two-parameter boundary problem for second order differential system

  • G. J. Etgen
  • S. C. Tefteller


This paper is concerned with second order differential systems involving two parameters with boundary conditions specified at three points. In particular, we consider the system y' = k(x, λ, μ)z, z' = -g(x, λ, μ)y, where k and g are real-valued junctions defined on X: a ≤ x ≤ c, L: L1 < λ < L2, and M: M1 < μ < M2. This system is studied together with the boundary conditions α(λ, μ)y(a) - β(λ, μ)z(a)=0, γ(λ, μ)y(b) - δ(λ, μ)z(b)=0, ε1(μ)y(b) - φ1(μ)z(b)=ε2(μ)y(c) - φ2(μ)z(c), where α, β, δ, γ, εi, φi, i=1, 2, are continuous functions of the parameters. This work establishes the existence of eigenvalue pairs for the boundary problem and the oscillatory behavior of the associated solutions. These results complement those previously obtained by the authors and B. D. Sleeman, where boundary conditions of the « Sturm-Liouville » type were studied.


Boundary Condition Continuous Function Boundary Problem Differential System Oscillatory Behavior 
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Copyright information

© Nicola Zanichelli Editore 1979

Authors and Affiliations

  • G. J. Etgen
    • 1
  • S. C. Tefteller
    • 1
  1. 1.HoustonU.S.A.

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