A two-parameter boundary problem for second order differential system
Annali Di Matematica Pura Ed Applicata(1979)
摘要
Summary 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 2, and M: M1 2. 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.
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关键词
sturm liouville,eigenvalues,boundary condition
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