Multivalued Equations

Ravi P. Agarwal and Donal O’Regan
Additional contact information
Ravi P. Agarwal: National University of Singapore
Donal O’Regan: University of Ireland

Chapter Chapter 7 in Infinite Interval Problems for Differential, Difference and Integral Equations, 2001, pp 294-328 from Springer

Abstract: Abstract This chapter presents an existence theory for multivalued nonlinear equations on the half line. In Section 7.2 we employ several recently established fixed point theorems to prove the existence of one (or more) C[0, ∞) solutions to the nonlinear integral inclusion (7.1.1) $$ x(t) \in \int_0^\infty {k(t,s)F(s,x(s))ds{\text{ for }}t \in [0,\infty ).}$$ Here k : [0,∞) × [0,∞) → ℝ and F : [0,∞) × ℝ → CK(ℝ) with CK(ℝ) denoting the family of nonempty, convex, compact subsets of ℝ. In Section 7.3 we investigate the topological structure of the solution set of the Volterra integral inclusion (7.1.2) $$ x(t) \in \int_0^t {k(t,s)F(s,x(s))ds{\text{ for }}t \in [0,\infty ).}$$ Here k : [0,∞) × [0,t] → ℝ and F : [0,∞) × ℝ n → CK(ℝ n ). In Section 7.4 we discuss the existence of solutions to the Fredholm integral inclusion (7.1.3) $$ x(t) \in h(t) + \int_0^\infty {k(t,s)F(s,x(s))ds{\text{ for }}t \in [0,\infty ).}$$ Here k(t,s) is a matrix valued kernel of type n by n and F : [0, ∞) × ℝ n → CK(ℝ n ). In Section 7.5 we establish the existence of C[0,τ) solutions to the abstract operator inclusions (7.1.4) $$ x(t) \in Vx(t) + \int_0^t {Wx(s)ds}$$ for t ∈ [0,τ] if 0

Keywords: Fixed Point Theorem; Differential Inclusion; Half Line; Existence Theory; Frechet Space (search for similar items in EconPapers)
Date: 2001
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-010-0718-4_7

Ordering information: This item can be ordered from
http://www.springer.com/9789401007184

DOI: 10.1007/978-94-010-0718-4_7

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().