“…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.…”
The aim of this paper is to show certain properties of the Green's functions related to the Hill's equation coupled with different two point boundary value conditions. We will obtain the expression of the Green's function of Neumann, Dirichlet, Mixed and anti-periodic problems as a combination of the Green's function related to periodic ones.As a consequence we will prove suitable results in spectral theory and deduce some comparison results for the solutions of the Hill's equation with different boundary value conditions.
“…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.…”
The aim of this paper is to show certain properties of the Green's functions related to the Hill's equation coupled with different two point boundary value conditions. We will obtain the expression of the Green's function of Neumann, Dirichlet, Mixed and anti-periodic problems as a combination of the Green's function related to periodic ones.As a consequence we will prove suitable results in spectral theory and deduce some comparison results for the solutions of the Hill's equation with different boundary value conditions.
“…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.…”
“…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).…”
Section: Advances In Mathematical Physicsmentioning
A boundary value problem for a stationary nonlinear dispersive equation of 2 + 1 order on an interval (0, ) was considered. The existence, uniqueness, and continuous dependence of a regular solution have been established.
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