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“…If we consider the periodic case with a(t) = π T 2 , using [5] we obtain the following expression for the Green's function…”
Section: Preliminariesmentioning
confidence: 99%
See 1 more Smart Citation
“…If we consider the periodic case with a(t) = π T 2 , using [5] we obtain the following expression for the Green's function…”
Section: Preliminariesmentioning
confidence: 99%
“…We can use [5] to calculate the Green's functions for the different boundary conditions Note that the eigenvalue of problem (M 2 , T ) always appears before the one of problem (M 1 , T ). In addition, the order between the eigenvalues of (N, T ) and (D, T ) is also maintained.…”
Section: Examplesmentioning
confidence: 99%
“…For negative values of M, we use the classical theory of disconjugacy [8], to obtain an estimate on M that ensures the negativeness of Green's function. To verify that the given estimation is optimal, by means of the Mathematica Package developed in [5] (see also [4]), we calculate the exact expression of the related Green's function. This study, combined with the spectral theory, is also applied to deduce that we cannot expect positive Green's functions for any value of the real parameter M.…”
Section: Introductionmentioning
confidence: 99%
“…It is known, [33,34], that (15) has a unique classical solution if and only if (16)- (17) has only the trivial solution. Let ∈ 2 +1 ([0, ]) be a nontrivial solution of (16)- (17).…”