Eigenvalues of boundary value problems for higher order differential equations

Patricia J. Y. Wong and Ravi P. Agarwal

Mathematical Problems in Engineering, 1996, vol. 2, 1-34

Abstract:

We shall consider the boundary value problem y ( n ) + λ Q ( t , y , y 1 , ⋅ ⋅ ⋅ , y ( n − 2 ) ) = λ P ( t , y , y 1 , ⋅ ⋅ ⋅ , y ( n − 1 ) ) , n ≥ 2 , t ∈ ( 0 , 1 ) , y ( i ) ( 0 ) = 0 , 0 ≤ i ≤ n − 3 , α y ( n − 2 ) ( 0 ) − β y ( n − 1 ) ( 0 ) = 0 , γ y ( n − 2 ) ( 1 ) + δ y ( n − 1 ) = 0 , where λ > 0 , α , β , γ and δ are constants satisfying α γ + α δ + β γ > 0 , β , δ ≥ 0 , β + α > 0 and δ + γ > 0 to characterize the values of λ so that it has a positive solution. For the special case λ = 1 , sufficient conditions are also established for the existence of positive solutions.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:952346

DOI: 10.1155/S1024123X96000415

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