  A graph $G$ is $H$-free, if it contains no $H$ as a subgraph. A graph is said
to be \emph{$H$-minor free}, if it does not contain $H$ as a minor. In recent
years, Nikiforov asked that what is the maximum spectral radius of an $H$-free
graph of order $n$? In this paper, we consider about some
Brualdi-Solheid-Tur\'{a}n type problems on bipartite graphs. In 2015, Zhai, Lin
and Gong proved that if $G$ is a bipartite graph with order $n \geq 2k+2$ and
$\rho(G)\geq \rho(K_{k,n-k})$, then $G$ contains a $C_{2k+2}$ unless $G \cong
K_{k,n-k}$ [Linear Algebra Appl. 471 (2015)]. Firstly, we give a new and more
simple proof for the above theorem. Secondly, we prove that if $G$ is a
bipartite graph with order $n \geq 2k+2$ and $\rho(G)\geq \rho(K_{k,n-k})$,
then $G$ contains all $T_{2k+3}$ unless $G \cong K_{k,n-k}$. Finally, we prove
that among all outerplanar bipartite graphs on $n>344569$ vertices, $K_{1,n-1}$
attains the maximum spectral radius.
