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Second-Order Differential Inclusions

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Method of Guiding Functions in Problems of Nonlinear Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2076))

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Abstract

Various aspects of the theory of second-order differential inclusions attract the attention of many researchers (see., e.g., [1, 2, 6, 12, 18, 42, 46, 47, 68, 70, 97]). In this chapter we consider the boundary value problem of form

$$\displaystyle{ {u}^{{\prime\prime}}\in Q(u),\;\;u(0) = u(1) = 0, }$$
(4.1)

for second-order differential inclusions which arises naturally from some physical and control problems. Using the method of guiding functions we study the existence of solutions of problem (4.1) in an one-dimensional and in Hilbert spaces.

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Authors and Affiliations

  1. Department of Physics and Mathematics, Voronezh State Pedagogical University, Voronezh, Russia

    Valeri Obukhovskii & Sergei Kornev

  2. Dipartimento di Matematica e Informatica “U Dini”, Università di Firenze, Firenze, Italy

    Pietro Zecca

  3. Faculty of Fundamental Science, PetroVietNam University, Ba Ria, Vietnam

    Nguyen Van Loi

Authors
  1. Valeri Obukhovskii
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  2. Pietro Zecca
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  3. Nguyen Van Loi
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  4. Sergei Kornev
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Obukhovskii, V., Zecca, P., Van Loi, N., Kornev, S. (2013). Second-Order Differential Inclusions. In: Method of Guiding Functions in Problems of Nonlinear Analysis. Lecture Notes in Mathematics, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37070-0_4

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