  Generalized trigonometric functions (GTFs) are simple generalization of the
classical trigonometric functions. GTFs are deeply related to the
$p$-Laplacian, which is known as a typical nonlinear differential operator, and
there are a lot of works on GTFs concerning the $p$-Laplacian. However, few
applications to differential equations unrelated to the $p$-Laplacian are
known. We will apply GTFs with two parameters to nonlinear nonlocal boundary
value problems without $p$-Laplacian. Moreover, we will give integral formulas
for the functions, e.g. Wallis-type formulas, and apply the formulas to the
lemniscate function and the lemniscate constant.
