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Second-Order Differential Inclusions

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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.

Keywords

  • Second-order Differential Inclusions
  • Boundary Value Problem
  • Multimap
  • Linear Fredholm Operator
  • Infinite Dimensional Real Hilbert Space

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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