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In this note new properties for the Gossez example are presented in regard to its representability, closedness, and maximal monotonicity with respect to the two dual systems it naturally inhabits., Keywords: monotone operator, dual system, Fitzpatrick function

Extensions of monotone operators into compact sets of a dual system are studied under general conditions.

Equivalent conditions that make the convex subdifferential maximal monotone are investigated in the general settings of locally convex spaces.

Our goal is to present a new shorter proof for the maximal monotonicity of the Minkowski sum of two maximal monotone multi-valued operators defined in a reflexive Banach space under the classical interiority condition involving their domains., Comment: 3 pages

This paper introduces new subdifferential concepts together with their main properties and place with respect to other subdifferential notions.

A result concerning global extrema in a nonsmooth nonconvex variational problem that appears in applications (e.g. in a large deformation elasticity problem) is investigated in comparison with a result of D.Y. Gao and R.W. Ogden. The tools used are elementary and the results derived improve upon and correct a recent similar result, more precisely, Theorem 4 of the paper "Closed-form solutions, extremality and nonsmoothness criteria in a large deformation elasticity problem" by the fore-mentioned authors., Comment: This paper has been submitted to ZAMP (Zeitschrift f\"ur angewandte Mathematik und Physik) on April 07, 2010 and was first rejected on December 08, 2010; then, on December 06, 2011 we get the decision "The Editorial Board of ZAMP does not want to pursue this matter any further", without any report. For more details see: http://www.math.uaic.ro/~zalinesc/

In the context of general Banach spaces characterizations for the maximal monotonicity of operators with non-empty domain interior as well as stronger continuity properties for such operators are provided.

In this note we prove that a recent result stated by D.Y. Gao and R.W. Ogden on global minimizers and local extrema in a phase transition problem is false. Our goal is achieved by providing a thorough analysis of the context and result in question and counter-examples., Comment: This paper has been submitted to QJMAM (The Quarterly Journal of Mechanics and Applied Mathematics) on February 19, 2010 and was rejected on October 19, 2010. The reason for the rejection was that "the paper is more like a pure math paper" and this decision was taken mainly after the editor investigated our web-pages. For more details see http://www.math.uaic.ro/~zalinesc/

The aim of this short note is to give counterexamples to two results by D. Y. Gao [5, Th. 16], [4, Th. 2] and to improve a related result by S.-C. Fang, D. Y. Gao, R.-L. Sheu and S.-Y. Wu [1, Th. 3]., Comment: This paper has been submitted to JIMO (Journal of Industrial and Management Optimization) on September 24, 2009 and rejected in May, 2010. The reason for the rejection was that " The authors' view on this issue is known to people in the field". See also http://www.math.uaic.ro/~zalinesc/

On [3, p. 199] one says "We mention parenthetically that the proof of [99, Lemma 41.3] is incorrect, and we do not know whether it, [99, Theorem 41.5] and [99, Theorem 41.6] are true". The previously cited reference [99] is our reference [2]. The aim of this short note is to provide a result that improves upon [2, Lemma 41. 3].

Recently in [1] a new class of maximal monotone operators has been introduced. In this note we study domain range properties as well as connections with other classes and calculus rules for these operators we called strongly-representable. While not every maximal monotone operator is strongly-representable, every maximal monotone NI operator is strongly-representable, and every strongly representable operator is locally maximal monotone, maximal monotone locally, and ANA. As a consequence the conjugate of the Fitzpatrick function of a maximal monotone operator is not necessarily a representative function.

The goal of this article is to give a positive answer to Rockafellar's maximality of the sum conjecture in the linear multi-valued operator case., 3 pages