Brezis-Browder Principles and Applications

Mihai Turinici ()
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Mihai Turinici: “A. Myller” Mathematical Seminar; “A. I. Cuza” University

Chapter Chapter 14 in Nonlinear Analysis and Variational Problems, 2010, pp 153-197 from Springer

Abstract: Abstract In Part 1, we show that the version of Brezis–Browder’s principle [Adv. Math., 21(1976), 355–364] for general separable sets is a logical equivalent of the Zorn–Bourbaki maximality result. Further, in Part 2, it is stressed that most (sequential) maximality principles are logical equivalents of that of Brezis–Browder; and the remaining ones, including Kang–Park’s [Nonlinear Analysis, 14 (1990), 159–165] may be viewed as particular cases of an “asymptotic” type version of Brezis–Browder’s principle. Finally, in Part 3, the variational statement due to Kada, Suzuki and Takahashi [Math. Japonica, 44 (1996), 381–391] is deduced from a “relative” type version of Brezis–Browder’s principle. The connections with some variational statements in Suzuki [J. Math. Anal. Appl., 253 (2001), 440–458], Lin and Du [J. Math. Anal. Appl., 323 (2006), 360–370] or Al-Homidan, Ansari and Yao [Nonlin. Anal., 69 (2008), 126–139] are also investigated.

Keywords: Maximality Principle; Variational Principle; Point Theorem; Regularity Condition; Maximal Element (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4419-0158-3_14

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DOI: 10.1007/978-1-4419-0158-3_14

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