Characterization of Eigenvalues for Difference Equations Subject to Lidstone Conditions
Wong, P.J.Y. Agarwal, R.P.
Wong, P.J.Y.
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Abstract
This paper considers the following boundary value problem (-1)mΔ2my = λF(k, y, Δy, . . . , Δ2m-1y), m ≥ 1, 0 ≤ k ≤ N Δ2iy(0) = Δ2iy(N + 2m - 2i) = 0, 0 ≤ i ≤ m - 1 where λ > 0. We characterize the values of λ so that the boundary value problem has a positive solution. Further, explicit intervals of λ are established so that for any λ in the interval, existence of a positive solution of the boundary value problem is assured. We also present several examples to dwell upon the importance of the results obtained.
Keywords
Boundary value problems, Eigenvalues, Positive solutions
Source Title
Japan Journal of Industrial and Applied Mathematics
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Date
2002-02
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Article