INTEGRAL CHARACTERIZATION OF THE PRINCIPAL SOLUTION O HALF-LINEAR SECOND ORDER DIF ERENTIAL EQUATIONS

2000 ◽  
Vol 36 (3-4) ◽  
pp. 455-469 ◽  
Author(s):  
O. DoŠlÝ ◽  
A. Elbert
Keyword(s):  
Nontrivial Solution ◽  
Second Order ◽  
Principal Solution ◽  
Sturm Liouville

Under some restrictions on the functions r (t)and c (t),a nontrivial solution x (t)of the nonoscillatory half-linear second order diferential equation: is principal if and only if… In case p =2 the criterion (*)reduces to a Hartman result on the principal solutions of the Sturm –Liouville di .erential equations.

scholarly journals NONTRIVIAL SOLUTIONS FOR STURM–LIOUVILLE SYSTEMS VIA A LOCAL MINIMUM THEOREM FOR FUNCTIONALS

2013 ◽  
Vol 89 (1) ◽  
pp. 8-18 ◽  
Author(s):  
GABRIELE BONANNO ◽  
SHAPOUR HEIDARKHANI ◽  
DONAL O’REGAN
Keyword(s):  
Nontrivial Solution ◽  
Local Minimum ◽  
Second Order ◽  
Nontrivial Solutions ◽  
Sturm Liouville ◽  
Minimum Theorem

AbstractIn this paper, employing a very recent local minimum theorem for differentiable functionals, the existence of at least one nontrivial solution for a class of systems of $n$ second-order Sturm–Liouville equations is established.

scholarly journals On the boundary conditions for products of Sturm-Liouville differential operators

2001 ◽  
Vol 32 (3) ◽  
pp. 187-199
Author(s):  
Sobhy El-Sayed Ibrahim
Keyword(s):  
Boundary Conditions ◽  
Differential Operators ◽  
Second Order ◽  
Regular Case ◽  
Sesquilinear Form ◽  
Sturm Liouville

In this paper, the second-order symmetric Sturm-Liouville differential expressions $ \tau_1, \tau_2, \ldots, \tau_n $ with real coefficients are considered on the interval $ I = (a,b) $, $ - \infty \le a < b \le \infty $. It is shown that the characterization of singular self-adjoint boundary conditions involves the sesquilinear form associated with the product of Sturm-Liouville differential expressions and elements of the maximan domain of the product operators, and is an exact parallel of the regular case. This characterization is an extension of those obtained in [6], [8], [11-12], [14] and [15].

scholarly journals On the domain of selfadjoint extension of the product of Sturm-Liouville differential operators

2003 ◽  
Vol 2003 (11) ◽  
pp. 695-709
Author(s):  
Sobhy El-Sayed Ibrahim
Keyword(s):  
Boundary Conditions ◽  
Differential Operators ◽  
Second Order ◽  
Regular Case ◽  
Maximal Domain ◽  
Selfadjoint Extension ◽  
Sesquilinear Form ◽  
Sturm Liouville

The second-order symmetric Sturm-Liouville differential expressionsτ1,τ2,…,τnwith real coefficients are considered on the intervalI=(a,b),−∞≤a<b≤∞. It is shown that the characterization of singular selfadjoint boundary conditions involves the sesquilinear form associated with the product of Sturm-Liouville differential expressions and elements of the maximal domain of the product operators, and it is an exact parallel of the regular case. This characterization is an extension of those obtained by Everitt and Zettl (1977), Hinton, Krall, and Shaw (1987), Ibrahim (1999), Krall and Zettl (1988), Lee (1975/1976), and Naimark (1968).

scholarly journals On the product of self-adjoint Sturm-Liouville differential operators in direct sum spaces

2006 ◽  
Vol 37 (1) ◽  
pp. 77-92 ◽  
Author(s):  
Sobhy El-Sayed Ibrahim
Keyword(s):  
Boundary Conditions ◽  
Finite Number ◽  
Differential Operators ◽  
Second Order ◽  
Regular Case ◽  
Maximal Domain ◽  
Direct Sum ◽  
Sesquilinear Form ◽  
Sturm Liouville

In this paper, the second-order symmetric Sturm-Liouville differential expressions $ \tau_1,\tau_2, \ldots, \tau_n $, with real coefficients on any finite number of intervals are studied in the setting of the direct sum of the $ L_w^2 $-spaces of functions defined on each of the separate intervals. It is shown that the characterization of singular self-adjoint boundary conditions involves the sesquilinear form associated with the product of Sturm-Liouville differential expressions and elements of the maximal domain of the product operators, it is an exact parallel of that in the regular case. This characterization is an extension of those obtained in [6], [7], [8], [9], [12], [14] and [15].

PMD Characterization of a Dispersion Managed Link up to the Second-order with High Accuracy

2006 ◽  
Vol 38 (7) ◽  
pp. 575-582
Author(s):  
O. M. Diaz ◽  
J. Prat ◽  
I. Tafur Monroy ◽  
H. de Waardt
Keyword(s):  
High Accuracy ◽  
Second Order
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