  Quite differently from those perturbation techniques in \cite{DM}, we use the
assumption of a $C^1$-stable critical point to construct positive or
sign-changing bubbling solutions to the boundary value problem $-\Delta
u=\lambda u|u|^{p-2}e^{|u|^p}$ with homogeneous Dirichlet boundary condition in
a bounded, smooth planar domain $\Omega$, when $0<p<2$ and $\lambda>0$ is a
small parameter. A sufficient condition on the intersection between the nodal
line of these sign-changing solutions and the boundary of the domain is
founded. Moreover, for $\lambda$ small enough, we prove that when $\Omega$ is
an arbitrary bounded domain, this problem has not only at least two pairs of
bubbling solutions which change sign exactly once and whose nodal lines
intersect the boundary, but also a bubbling solution which changes sign exactly
twice or three times; when $\Omega$ has an axial symmetry, this problem has a
bubbling solution which alternately changes sign arbitrarily many times along
the axis of symmetry through the domain.
