Calderon's Reproducing Formula Associated with a Singular Differential Operator on the Half Line

2000 ◽  
Vol 10 (2) ◽  
pp. 101-114 ◽  
Author(s):  
Mohamed A. Mourou ◽  
Khalifa Triméche
Keyword(s):  
Differential Operator ◽  
Half Line ◽  
Singular Differential Operator ◽  
Calderón’S Reproducing Formula

On the deficiency indices of a fourth order singular differential operator

1979 ◽  
Vol 84 (1-2) ◽  
pp. 173-176
Author(s):  
Alastair D. Wood
Keyword(s):  
Differential Operator ◽  
Fourth Order ◽  
Half Line ◽  
Real Numbers ◽  
Singular Differential Operator ◽  
The Real ◽  
Deficiency Indices

SynopsisWe consider the operatorL[y] =y(4)+ ((ax2+bx+c)y′)′ +dyon the half-line [0, ∞). This paper shows that the deficiency indices are independent of the real numbersb, canddwhena≠ 0. They depend only on the sign ofaand are (2,2) ifa< 0 and (3, 3) ifa> 0. In the casea=0 the sign ofbmust be considered.

On an Invertible Extension of a Nonself-Adjoint Singular Differential Operator on the Half-Line

2021 ◽  
Vol 57 (10) ◽  
pp. 1408-1412
Author(s):  
L. K. Kussainova ◽  
Ya. T. Sultanaev ◽  
A. S. Kassym
Keyword(s):  
Differential Operator ◽  
Half Line ◽  
Singular Differential Operator

scholarly journals On a fractional-order p-Laplacian boundary value problem at resonance on the half-line with two dimensional kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
O. F. Imaga ◽  
S. A. Iyase
Keyword(s):  
Differential Operator ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Half Line ◽  
At Resonance ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Problem At Resonance

AbstractIn this work, we consider the solvability of a fractional-order p-Laplacian boundary value problem on the half-line where the fractional differential operator is nonlinear and has a kernel dimension equal to two. Due to the nonlinearity of the fractional differential operator, the Ge and Ren extension of Mawhin’s coincidence degree theory is applied to obtain existence results for the boundary value problem at resonance. Two examples are used to validate the established results.

Semibounded Extensions of Singular Ordinary Differential Operators

1988 ◽  
Vol 31 (4) ◽  
pp. 432-438
Author(s):  
Allan M. Krall
Keyword(s):  
Differential Operator ◽  
Lower Bound ◽  
Boundary Conditions ◽  
Differential Operators ◽  
The Self ◽  
Limit Circle ◽  
Singular Differential Operator ◽  
Ordinary Differential Operators

AbstractThe self-adjoint extensions of the singular differential operator Ly = [(py’)’ + qy]/w, where p < 0, w > 0, q ≧ mw, are characterized under limit-circle conditions. It is shown that as long as the coefficients of certain boundary conditions define points which lie between two lines, the extension they help define has the same lower bound.

17.—The Limit-point and Limit-circle Cases for Polynomials in a Differential Operator

1975 ◽  
Vol 72 (3) ◽  
pp. 219-224 ◽  
Author(s):  
Anton Zettl
Keyword(s):  
Differential Operator ◽  
Differential Expression ◽  
Limit Point ◽  
Half Line ◽  
Limit Circle

SynopsisThis paper is concerned with the L2 classification of ordinary symmetrical differential expressions defined on a half-line [0, ∞) and obtained from taking formal polynomials of symmetric differential expression. The work generalises results in this area previously obtained by Chaudhuri, Everitt, Giertz and the author.

ASYMPTOTICS FOR NONLINEAR NONLOCAL EQUATIONS ON A HALF-LINE

2006 ◽  
Vol 08 (02) ◽  
pp. 189-217 ◽  
Author(s):  
ROSA E. CARDIEL ◽  
ELENA I. KAIKINA ◽  
PAVEL I. NAUMKIN
Keyword(s):  
Differential Operator ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Inverse Laplace Transform ◽  
Half Line ◽  
Pseudo Differential Operator ◽  
Representation Of Solutions ◽  
Initial Boundary Value

We study the initial-boundary value problem for a general class of nonlinear pseudo-differential equations on a half-line [Formula: see text] where the number M depends on the order of the pseudo-differential operator [Formula: see text] on a half-line. The nonlinear term [Formula: see text] is such that [Formula: see text] as u, v → 0, with ρ, σ > 0. Pseudo-differential operator [Formula: see text] is defined by the inverse Laplace transform. The aim of this paper is to prove the global existence of solutions to the initial-boundary value problem (0.1) and to find the main term of the asymptotic representation of solutions taking into account the influence of inhomogeneous boundary data and a source on the asymptotic properties of solutions.

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