Results 271 to 280 of about 1,223,903 (308)
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2009
Linear differential equations are simpler in many respects. The truth of this statement is already obvious from the fact that their solution spaces possess the structure of a vector space. Thus it is not surprising that some of our previous results may be improved in this special case.
Richard Bronson, Gabriel B. Costa
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Linear differential equations are simpler in many respects. The truth of this statement is already obvious from the fact that their solution spaces possess the structure of a vector space. Thus it is not surprising that some of our previous results may be improved in this special case.
Richard Bronson, Gabriel B. Costa
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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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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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1966
Publisher Summary This chapter focuses on higher-order linear equations. Even for second-order linear equations, no general method of solution is available as there was for first-order equations. Formulas for general solutions can be found for certain special classes of higher-order equations.
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Publisher Summary This chapter focuses on higher-order linear equations. Even for second-order linear equations, no general method of solution is available as there was for first-order equations. Formulas for general solutions can be found for certain special classes of higher-order equations.
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Solvability of Linear Differential Equations
Дифференциальные уравнения, 2023We propose a new approach to the solvability of ordinary as well as partial differential equations in the theory of linear differential equations and also in the theory of integral equations.
Mokeichev, V. S., Sidorov, A. M.
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2017
In this chapter we obtain corresponding results to those in Chapter 3 for continuous time. More precisely, we study in detail the class of Lyapunov exponents defined by the solutions of a nonautonomous linear equation. In particular, we obtain lower and upper bounds for the Grobman coefficient.
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In this chapter we obtain corresponding results to those in Chapter 3 for continuous time. More precisely, we study in detail the class of Lyapunov exponents defined by the solutions of a nonautonomous linear equation. In particular, we obtain lower and upper bounds for the Grobman coefficient.
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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
openaire +1 more source