The following will display what you want, but only allow you to refer to all four together, but not individually like (4a) or (4c).
\documentclass{article}
\usepackage{amsmath}
\begin{document}
First put in a normal equation
\begin{equation}
E = mc^2
\end{equation}
Then the weird one:
\begin{equation}
u(0)=u_1; \qquad \phi(0)=-\phi_1; \qquad u(L)=u_2; \qquad \phi(L) = -\phi_2,
\refstepcounter{equation}\tag{\theequation a-d}\label{eq:35}
\end{equation}
The above is \eqref{eq:35}. Then another one to make sure the numbering is ok.
\begin{equation}
K = \frac12 mv^2
\end{equation}
\end{document}

Version 2: if you want to refer to individual ones, you can do worse than steal from egreg.
\documentclass{article}
\usepackage{amsmath}
\AtBeginDocument{\let\latexlabel\label}
\begin{document}
First put in a normal equation
\begin{equation}
E = mc^2
\end{equation}
Then the weird one:
\begin{subequations}\label{eq:all}
\[
\refstepcounter{equation}\latexlabel{eq:partA}
\refstepcounter{equation}\latexlabel{eq:partB}
\refstepcounter{equation}\latexlabel{eq:partC}
\refstepcounter{equation}\latexlabel{eq:partD}
u(0)=u_1; \qquad \phi(0)=-\phi_1; \qquad u(L)=u_2; \qquad \phi(L) = -\phi_2,
\tag{\ref{eq:partA}--\ref{eq:partD}}
\]
\end{subequations}
The above is \eqref{eq:all}, which is composed of \eqref{eq:partA}, \eqref{eq:partB}, \eqref{eq:partC}, \eqref{eq:partD}. Then another one to make sure the numbering is ok.
\begin{equation}
K = \frac12 mv^2
\end{equation}
\end{document}
Writing it like this you get separate reference points for the entire set eq:all and the individual ones.

\usepackage{amsmath}and do\tag{4a-d}. If you want the counter to be autoincremented (so that if you add a different displayed equation before you will automatically change from4to5, and if you want reasonable outputs when you say\ref, then it will need more work. Please be precise about all the features you will need. – Willie Wong Jul 19 '16 at 14:06