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Second-Order Differential Inclusions

  • Valeri Obukhovskii
  • Pietro Zecca
  • Nguyen Van Loi
  • Sergei Kornev
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2076)

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Valeri Obukhovskii
    • 1
  • Pietro Zecca
    • 2
  • Nguyen Van Loi
    • 3
  • Sergei Kornev
    • 1
  1. 1.Department of Physics and MathematicsVoronezh State Pedagogical UniversityVoronezhRussia
  2. 2.Dipartimento di Matematica e Informatica “U Dini”Università di FirenzeFirenzeItaly
  3. 3.Faculty of Fundamental SciencePetroVietNam UniversityBa RiaVietnam

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