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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.
Hartmut Logemann, Eugene P. Ryan
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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.
Hartmut Logemann, Eugene P. Ryan
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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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1967
In this section we consider the vector equation $$ \mathop x\limits^. {\rm{ }} = {\rm{ }}A(t){\rm{ }}. $$ (58.1) We assume that the elements a i k (t) of the matrix A are continuous functions of t defined for t ≥ t0. Equations with a constant A, treated in sec. 4, are special cases of (58.1). On the other hand, (58.1) is a special case of the
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In this section we consider the vector equation $$ \mathop x\limits^. {\rm{ }} = {\rm{ }}A(t){\rm{ }}. $$ (58.1) We assume that the elements a i k (t) of the matrix A are continuous functions of t defined for t ≥ t0. Equations with a constant A, treated in sec. 4, are special cases of (58.1). On the other hand, (58.1) is a special case of the
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1993
Consider the linear differential equation $$ u^{(n)} = p(t)u $$ (1.1) where. As a rule we assume that either $$ p(t) \leqslant 0 for t \in R_ + $$ (1.2) or $$ p(t) \geqslant 0 for t \in R_ + . $$ (1.3) A solution of (1.1) is said to be oscillatory if it has infinitely many zeros.
I. T. Kiguradze, T. A. Chanturia
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Consider the linear differential equation $$ u^{(n)} = p(t)u $$ (1.1) where. As a rule we assume that either $$ p(t) \leqslant 0 for t \in R_ + $$ (1.2) or $$ p(t) \geqslant 0 for t \in R_ + . $$ (1.3) A solution of (1.1) is said to be oscillatory if it has infinitely many zeros.
I. T. Kiguradze, T. A. Chanturia
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1992
Let us consider the n-th order linear differential equation $$L\left[ y \right] = {y^{\left( n \right)}} + {a_1}{y^{\left( {n - 1} \right)}} + \ldots + {a_{n - 1}}y' + {a_n}y = f$$ where a l, a 2,..., a n, f ∈ C([a,b]) are given.
Gheorghe Micula, Paraschiva Pavel
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Let us consider the n-th order linear differential equation $$L\left[ y \right] = {y^{\left( n \right)}} + {a_1}{y^{\left( {n - 1} \right)}} + \ldots + {a_{n - 1}}y' + {a_n}y = f$$ where a l, a 2,..., a n, f ∈ C([a,b]) are given.
Gheorghe Micula, Paraschiva Pavel
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IEEE/ACM Transactions on Computational Biology & Bioinformatics, 2008
H. Jong, M. Page
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H. Jong, M. Page
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The Use of Volterra Series to Find Region of Stability of a Non-linear Differential Equation†
, 1965J. Barrett
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