Nontrivial Solutions of Abstract Hammerstein Equations

Radu Precup
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Radu Precup: Babeş-Bolyai University, Department of Applied Mathematics

Chapter Chapter 9 in Methods in Nonlinear Integral Equations, 2002, pp 129-144 from Springer

Abstract: Abstract This chapter deals with nontrivial solvability in balls of abstract Hammer-stein equations and Hammerstein integral equations in R n by a variational approach. The variational method for treating Hammerstein integral equations goes back to the papers of Hammerstein [17] and Golomb [15]. For further contributions see the monographs by Krasnoselskii [19], Krasnoselskii-Zabreiko-Pustylnik-Sobolevskii [20] and Vainberg [43]. For more recent results see the papers by Moroz-Vignoli-Zabreiko [24] and Moroz-Zabreiko [25], [26]. The results presented in this chapter were adapted from Precup [31]–[34].

Keywords: Nontrivial Solution; Linear Partial Differential Equation; Mountain Pass Theorem; Continuous Embedding; Apply Theorem (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-94-015-9986-3_10

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