Geodesic
Theoretical foundations of the study of a certain class of hybrid systems of differential equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical Analysis, Tome 155 (2018), pp. 38-64

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In this paper, we consider boundary-value problems for a new class of hybrid systems of differential equations whose coefficients contain the Dirac delta-function. Hybrid systems are systems that contain both ordinary and partial differential equations; such systems appear, for example, when equations of motion of mechanical systems of rigid bodies attached to a rod by elastic bonds are derived from the Hamilton–Ostrogradsky variational principle. We present examples that lead to such systems and introduce the notions of generalized solutions and eigenvalues of a boundary-value problem. We also compare results of numerical simulations based on methods proposed in this paper with results obtained by previously known methods and show that our approach is reliable and universal.
Keywords: eigenvalue, boundary-value problem, hybrid system, differential equation, frequency equation. 
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     author = {A. D. Mizhidon},
     title = {Theoretical foundations of the study of a certain class of hybrid systems of differential equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {38--64},
     publisher = {mathdoc},
     volume = {155},
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A. D. Mizhidon. Theoretical foundations of the study of a certain class of hybrid systems of differential equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical Analysis, Tome 155 (2018), pp. 38-64. http://geodesic.mathdoc.fr/item/INTO_2018_155_a2/