Solvability of a degenerate differential equation with spectral parameter

1986 ◽  
Vol 25 (2) ◽  
pp. 162-165 ◽  
Author(s):  
J. Macionis
Keyword(s):  
Differential Equation ◽  
Spectral Parameter ◽  
Degenerate Differential Equation

scholarly journals On nonlocal perturbation of the problem on eigenvalues of differentiation operator on a segment

2021 ◽  
Vol 31 (2) ◽  
pp. 186-193
Author(s):  
N.S. Imanbaev
Keyword(s):  
Differential Equation ◽  
Spectral Problem ◽  
Characteristic Polynomial ◽  
Spectral Parameter ◽  
Order Differential Equation ◽  
Differentiation Operator ◽  
First Order ◽  
Entire Analytic Function ◽  
Polynomial Formula ◽  
Integral Perturbation

This work is devoted to the construction of a characteristic polynomial of the spectral problem of a first-order differential equation on an interval with a spectral parameter in a boundary value condition with integral perturbation which is an entire analytic function of the spectral parameter. Based on the characteristic polynomial formula, conclusions about the asymptotics of the spectrum of the perturbed spectral problem are established.

scholarly journals Boundary Value Problem for Weak Nonlinear Partial Differential Equations of Mixed Type with Fractional Hilfer Operator

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 68 ◽  
Author(s):  
Tursun K. Yuldashev ◽  
Bakhtiyor J. Kadirkulov
Keyword(s):  
Differential Equation ◽  
Fourier Series ◽  
Boundary Value Problem ◽  
Spectral Parameter ◽  
Mixed Type ◽  
Boundary Value ◽  
Nonlinear Partial Differential Equation ◽  
Rectangular Domain ◽  
Partial Differential ◽  
Negative Part

In this paper, we consider a boundary value problem for a nonlinear partial differential equation of mixed type with Hilfer operator of fractional integro-differentiation in a positive rectangular domain and with spectral parameter in a negative rectangular domain. With respect to the first variable, this equation is a nonlinear fractional differential equation in the positive part of the considering segment and is a second-order nonlinear differential equation with spectral parameter in the negative part of this segment. Using the Fourier series method, the solutions of nonlinear boundary value problems are constructed in the form of a Fourier series. Theorems on the existence and uniqueness of the classical solution of the problem are proved for regular values of the spectral parameter. For irregular values of the spectral parameter, an infinite number of solutions of the mixed equation in the form of a Fourier series are constructed.

scholarly journals Optimal time and space regularity for solutions of degenerate differential equations

2009 ◽  
Vol 7 (2) ◽  
Author(s):  
Alberto Favaron
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Cauchy Problem ◽  
Differential Equations ◽  
Optimal Time ◽  
Time And Space ◽  
Optimal Regularity ◽  
Degenerate Differential Equation ◽  
The Cauchy Problem ◽  
Degenerate Differential Equations

AbstractWe derive optimal regularity, in both time and space, for solutions of the Cauchy problem related to a degenerate differential equation in a Banach space X. Our results exhibit a sort of prevalence for space regularity, in the sense that the higher is the order of regularity with respect to space, the lower is the corresponding order of regularity with respect to time.

10.—Generalisation of Some Statements by Kodaira

1973 ◽  
Vol 71 (2) ◽  
pp. 113-119
Author(s):  
Christer Bennewitz
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Spectral Parameter ◽  
Differential Operators ◽  
Ordinary Linear Differential Equation ◽  
Ordinary Differential Operators ◽  
Linear Differential

SynopsisThis paper presents a generalisation of earlier results on the dimension of the space of integrable-square solutions of the ordinary linear differential equation Su = λTu, where S and T are formally symmetric ordinary differential operators and λ is a spectral parameter.

scholarly journals Fractional differential equation with a complex potential

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1731-1737
Author(s):  
Ekin Uğurlu ◽  
Kenan Taşa ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Potential Function ◽  
Spectral Parameter ◽  
Complex Potential ◽  
Linearly Independent ◽  
Fractional Differential ◽  
Complex Valued

In this manuscript, we discuss the square-integrable property of a fractional differential equation having a complex-valued potential function and we show that at least one of the linearly independent solutions of the fractional differential equation must be squarely integrable with respect to some function containing the imaginary parts of the spectral parameter and the potential function.

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