Results 171 to 180 of about 182,959 (213)
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Linear distribution differential equations
Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 1984Let \(c\in {\mathbb{R}}\), let \({\mathcal P}^ 0\) be the set of Borel measures with support in \(x\leq c\). Let \({\mathcal B}^ 0\) be the set of all locally bounded Borel measurable functions with support in \(x\geq c\). Let \(\mu\in {\mathcal D}'({\mathbb{R}})\). Let \(j\geq 0\) be an integer. If for some \(\eta\in {\mathcal P}^ 0\) \(D^ j\mu =\eta\)
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On Systems of Linear Differential Equations
American Journal of Mathematics, 1951with U a column vector and A and P n-square matrices. The transformation U = TU, by a unimodular matrix T is easily seen to result in an equation in U, of form (1), in which the coefficient of A is T-1AT. It is known [1] that if the elements of A and its characteristic roots are holomorphic in a closed bounded region R, then there exists a matrix T ...
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On the Meromorphic Solutions of Linear Differential Equations
Journal of Systems Science and Complexity, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On liouvillian solutions of linear differential equations
Applicable Algebra in Engineering, Communication and Computing, 1992Let \(L(y)=0\) be a homogeneous linear differential equation and \(R(z)=0\) be the associated Riccati equation. The paper deals with the problem of finding the possible degrees of the minimal polynomial of an algebraic solution of \(R(z)=0\). Supposing that \(L(y)\) is irreducible and \(L(y)=0\) has a Liouvillian solution, the author obtains sharp ...
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2016
In this chapter we deal with some basic facts concerning ordinary linear differential equations in the analytic domain, culminating in Fuchs’ theory on regular singular points.
Anish Deb +2 more
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In this chapter we deal with some basic facts concerning ordinary linear differential equations in the analytic domain, culminating in Fuchs’ theory on regular singular points.
Anish Deb +2 more
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On Linear Perturbation of Non-Linear Differential Equations
Canadian Journal of Mathematics, 1954In the theory of the asymptotic solution or stability of ordinary differential equations most attention has been given to linear or nearly-linear cases. Investigations in this field, starting primarily with those of Kneser(7)on the equation y″+f(x)y= 0, have by now mostly been summed up in results on the vector-matrix system dy/dx =Ay +f(y,x ...
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2014
For linear differential equations, the structures of solution spaces are characterized and solution formulas are derived in terms of fundamental matrix solutions. The calculations of fundamental matrix solutions are studied for the constant coefficient case and the Floquet theory is presented for the periodic coefficient case.
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For linear differential equations, the structures of solution spaces are characterized and solution formulas are derived in terms of fundamental matrix solutions. The calculations of fundamental matrix solutions are studied for the constant coefficient case and the Floquet theory is presented for the periodic coefficient case.
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2001
Here we consider a so called (scalar) normal system of n ordinary linear differential equations which is a system of the form $$\left\{ {\begin{array}{*{20}{c}} {{{{x'}}_{1}} = {{a}_{{11}}}(t){{x}_{1}} + {{a}_{{12}}}(t){{x}_{2}} + ... + {{a}_{{1n}}}(t){{x}_{n}} + {{f}_{1}}(t),} \\ {{{{x'}}_{2}} = {{a}_{{21}}}(t){{x}_{1}} + {{a}_{{22}}}(t){{x}_{2}} +
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Here we consider a so called (scalar) normal system of n ordinary linear differential equations which is a system of the form $$\left\{ {\begin{array}{*{20}{c}} {{{{x'}}_{1}} = {{a}_{{11}}}(t){{x}_{1}} + {{a}_{{12}}}(t){{x}_{2}} + ... + {{a}_{{1n}}}(t){{x}_{n}} + {{f}_{1}}(t),} \\ {{{{x'}}_{2}} = {{a}_{{21}}}(t){{x}_{1}} + {{a}_{{22}}}(t){{x}_{2}} +
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Remarks on the Linearization of Differential Equations
IMA Journal of Applied Mathematics, 1977openaire +2 more sources