For detailed information about the properties and options of the elsarticle document class, I recommend you bring up a command window and type
texdoc elsarticle
and start reading the user guide for this document class.
For sure, I would not specify the options final, 5p, and twocolumn. Instead, I would try
\documentclass[times]{elsarticle}
The default options, i.e., those that needn't be specified explicitly in order to be in effect, are a4paper, 10pt, oneside, onecolumn and preprint. For a journal submission, it may also be unnecessary to specify times (an option for the text font to be used in the document).
The optional argument to the \author macro in the elsarticle class is used to indicate the affiliation (address) of each author. Each number is supposed to be a reference to an \address. So, if each author had one address:
\author[1]{Don Joe}
\author[2]{Smith K.}
\address[1]{Address of Don Joe}
\address[2]{Address of Smith K.}
each address would be superscripted to an author, no matter the order you give them. You can also specify multiple affiliations for one single author:
\author[1,3]{Don Joe}
\author[2,3]{Smith K.}
\address[1]{Address of Don Joe}
\address[2]{Address of Smith K.}
\address[3]{Department of John Doe and Smith K.}
here each author would have two superscripts, John Doe would have a,c, and Smith K., b,c.
This works more or less in the same fashion as LaTeX references. You give a "label" to the \address and put one (or more) \ref in each \author.
But, as you said, the authors all have the same address, so only one address line is needed:
\address[1]{Address of all authors}
and all authors have the reference to this address:
\author[1]{Don Joe}
\author[1]{Smith K.}
\author[1]{Wanderer}
\author[1]{Static}
But this would put a superscript a on each author:
So maybe it will look better if you don't use the "label-ref" system at all:
\documentclass[3p,times]{elsarticle}
% \usepackage{ecrc}
\usepackage{amssymb}
\usepackage{amsmath}
\begin{document}
\begin{frontmatter}
\title{This is Title}
\author{Don Joe}
\author{Smith K.}
\author{Wanderer}
\author{Static}
\address{Address of all authors}
\end{frontmatter}
\end{document}
which produces:
which, in my opinion, looks less redundant than the other alternative.
Actually, the numbers don't necessarily need to be numbers. You put anything that is a valid letter for a TeX macro name. For example, this:
\author [1]{Don Joe}
\author [1]{Smith K.}
\author [1]{Wanderer}
\author [1]{Static}
\address[1]{tex.stackexchange.com}
produces exactly the same output as this:
\author [duckland]{Don Joe}
\author [duckland]{Smith K.}
\author [duckland]{Wanderer}
\author [duckland]{Static}
\address[duckland]{tex.stackexchange.com}
Also, I suppose you are using elsarticle to submit a paper to one of Elsevier's journals. In this case, you don't have to worry too much about this, because the final formatting of the paper is done by them, so it shouldn't matter the presence or not of the superscripted 1, as long as you give the affiliations correctly when submitting the paper :)
Best Answer
You need to annotate
\authorstatements.