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On the relationship between the initial and the multipoint boundary value problems for \(n\)-th-order linear differential equations of neutral type. (English) Zbl 0961.34070

Summary: The author gives some relationship between the initial value problems and Haščák’s boundary value problems for linear differential equations of neutral type [A. Haščák, J. Math. Anal. Appl. 199, No. 2, 323-333 (1996; Zbl 0853.34061)].

MSC:

34K40 Neutral functional-differential equations
34K06 Linear functional-differential equations
34K10 Boundary value problems for functional-differential equations

Citations:

Zbl 0853.34061
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References:

[1] Gel’fond A. O.: Calculus of Finite Differences. Moscow 1952 (in Russian). Delhi 1971
[2] Haščák A.: Disconjugacy and Multipoint Boundary Value Problems for Linear Differential Equations with Delay. Czech. Math. J. 39, 14 (1989), 70-77. · Zbl 0689.34058
[3] Haščák A.: Tests for Disconjugacy and Strict Disconjugacy of Linear Differential Equations with Delays. Czech. Math. J. 114, 39 (1989), 225-231. · Zbl 0703.34072
[4] Haščák A.: On the Relationship between the Initial and Multipoint Boundary Value Problems for n-th Order Linear Differential Equations with Delay. Arch. Math. (Brno) 26, 4 (1990), 207-214. · Zbl 0731.34077
[5] Haščák A.: Disconjugacy and Multipoint Boundary Value Problems for Linear Differential Equations of Neutral Type. Journal of Mathematical Analysis and Applications 199 (1996), 323-333. · Zbl 0853.34061
[6] Haščák A.: Test for Disconjugacy of a Differential Inclusion of Neutral Type. Georgian Math. J. 4, 2 (1997), 101-108. · Zbl 0870.34020
[7] Lasota A.: A Note on the Relationship between the Initial and the Boundary Value Problems for Ordinary Differential Equations of the n-th Order. Zeszity naukowe Universsitetu Jagielonskiego 22 (1959), Poland, 59-65
[8] Norkin S. B.: Differential Equations of Second Order with Deviating Arguments. Nauka, Moscow, 1965.
[9] Staněk S.: On some Boundary Value Problems for Second Order Functional Differential Equations. Nonlinear Analysis, Theory, Methods and Applications 28, 3 (1997), 539-546. · Zbl 0873.34053
[10] Staněk S.: On a Class of Functional Boundary Value Problems for Second-order Functional Differential Equations with Parameter. Czech. Math. J. 43, 118 (1993), 339-348. · Zbl 0788.34069
[11] Rachůnková I., Staněk S.: Topological Degree Method in Functional Boundary Value Problems. Nonlin. Anal. 27 (1996), 271-285. · Zbl 0853.34062
[12] Rachůnková I., Staněk S.: Topological Degree Method in Functional Boundary Value Problems at Resonance. Nonlin. Anal. 28 (1997), 539-546.
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