scholarly journals On the mild solutions of higher-order differential equations in Banach spaces

2003 ◽  
Vol 2003 (15) ◽  
pp. 865-880 ◽  
Author(s):  
Nguyen Thanh Lan
Keyword(s):  
Differential Equation ◽  
Banach Spaces ◽  
Mild Solutions ◽  
Higher Order ◽  
Almost Periodicity ◽  
Abstract Differential Equation ◽  
Translation Invariant ◽  
Definition Of ◽  
Translation Invariant Subspace ◽  
Higher Order Differential Equations

For the higher-order abstract differential equationu(n)(t)=Au(t)+f(t),t∈ℝ, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspaceℳofBUC(ℝ,E)with respect to the above-mentioned equation in terms of solvability of the operator equationAX−X𝒟n=C. As applications, periodicity and almost periodicity of mild solutions are also proved.

scholarly journals Bounded solutions of nonlinear Cauchy problems

2002 ◽  
Vol 7 (12) ◽  
pp. 637-661 ◽  
Author(s):  
Josef Kreulich
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Existence Of Solutions ◽  
Continuous Functions ◽  
Almost Periodicity ◽  
Cauchy Problems ◽  
Bounded Solutions ◽  
Translation Invariant ◽  
Uniformly Continuous ◽  
Translation Invariant Subspace

For a given closed and translation invariant subspaceYof the bounded and uniformly continuous functions, we will give criteria for the existence of solutionsu∈Yto the equationu′(t)+A(u(t))+ωu(t)∍f(t),t∈ℝ, or of solutionsuasymptotically close toYfor the inhomogeneous differential equationu′(t)+A(u(t))+ωu(t)∍f(t),t>0,u(0)=u0, in general Banach spaces, whereAdenotes a possibly nonlinear accretive generator of a semigroup. Particular examples for the spaceYare spaces of functions with various almost periodicity properties and more general types of asymptotic behavior.

scholarly journals New Properties of Modified Second Kind Chebyshev Polynomials

2020 ◽  
Vol 55 (3) ◽  
Author(s):  
Semaa Hassan Aziz ◽  
Mohammed Rasheed ◽  
Suha Shihab
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Chebyshev Polynomial ◽  
Chebyshev Polynomials ◽  
Digital Computer ◽  
Higher Order ◽  
Algebraic Equations ◽  
Equation Problem ◽  
Higher Order Differential Equations

Modified second kind Chebyshev polynomials for solving higher order differential equations are presented in this paper. This technique, along with some new properties of such polynomials, will reduce the original differential equation problem to the solution of algebraic equations with a straightforward and computational digital computer. Some illustrative examples are included. The modified second kind Chebyshev polynomial is calculated using only a small number of the modified second kind Chebyshev polynomials, which leads to attractive results.

scholarly journals Switching Point Solution of Second-Order Fuzzy Differential Equations Using Differential Transformation Method

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 231 ◽  
Author(s):  
Nadeem Salamat ◽  
Muhammad Mustahsan ◽  
Malik Saad Missen
Keyword(s):  
Differential Equations ◽  
Numerical Technique ◽  
Transformation Method ◽  
Higher Order ◽  
Differential Transformation Method ◽  
Fuzzy Differential Equation ◽  
Differential Transformation ◽  
Point Solution ◽  
Definition Of ◽  
Higher Order Differential Equations

The first-order fuzzy differential equation has two possible solutions depending on the definition of differentiability. The definition of differentiability changes as the product of the function and its first derivative changes its sign. This switching of the derivative’s definition is handled with the application of min, max operators. In this paper, a numerical technique for solving fuzzy initial value problems is extended to solving higher-order fuzzy differential equations. Fuzzy Taylor series is used to develop the fuzzy differential transformation method for solving this problem. This leads to a single solution for higher-order differential equations.

scholarly journals Nonlinear definition of the shadowy mode in higher-order scalar-tensor theories

2021 ◽  
Vol 2021 (12) ◽  
pp. 020
Author(s):  
Antonio De Felice ◽  
Shinji Mukohyama ◽  
Kazufumi Takahashi
Keyword(s):  
Differential Equation ◽  
Coordinate System ◽  
Three Dimensional ◽  
Spacelike Hypersurface ◽  
Higher Order ◽  
Elliptic Differential Equation ◽  
Unitary Gauge ◽  
Definition Of

Abstract We study U-DHOST theories, i.e., higher-order scalar-tensor theories which are degenerate only in the unitary gauge and yield an apparently unstable extra mode in a generic coordinate system. We show that the extra mode satisfies a three-dimensional elliptic differential equation on a spacelike hypersurface, and hence it does not propagate. We clarify how to treat this “shadowy” mode at both the linear and the nonlinear levels.

On the eigenvectors for a class of matrices arising from quasi-derivatives

1984 ◽  
Vol 97 ◽  
pp. 73-78 ◽  
Author(s):  
M. S. P. Eastham
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Asymptotic Theory ◽  
Higher Order ◽  
Symmetric Matrices ◽  
Convenient Formula ◽  
Class Of Matrices ◽  
Higher Order Differential Equations

SynopsisLet A be a product of symmetric matrices, A = RQ, with R non-singular, and let v be an eigenvector of A. For certain R and Q, a convenient formula for the expression (R−1v)tv is obtained. This expression occurs in the diagonalization of A and, in the particular case where A is associated with the quasi-derivative formulation of higher-order differential equations, the expression occurs in the asymptotic theory of solutions of the differential equation.

scholarly journals Twin positive solutions for three-point boundary value problems of higher-order differential equations

2004 ◽  
Vol 2004 (39) ◽  
pp. 2049-2063
Author(s):  
Yuji Liu ◽  
Weigao Ge
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Higher Order ◽  
Point Boundary ◽  
Higher Order Differential Equations

A new fixed point theorem on cones is applied to obtain the existence of at least two positive solutions of a higher-order three-point boundary value problem for the differential equation subject to a class ofboundary value conditions. The associated Green's function is given. Some results obtained recently are generalized.

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