Journal of the
Korean Mathematical Society JKMS

In this paper, the multiplicity, stability and the structure of classical solutions of semilinear elliptic equations of the form
$$\begin{cases} \Delta u+f(x,u)=0\quad\text{in}\quad\Omega,\\
u=0\quad\text{on}\quad\partial\Omega\end{cases}$$
will be discussed. Here $\Omega$ is a smooth and bounded domain in $ \bf R^n(n\ge 1) $, $f(x,u)=|u|^\alpha\text{sgn}(u)-h(x)$,
$0<\alpha<1$, $(n\ge 1)$ and $h$ is a $\tau$- H\"older continuous function on $\bar\Omega$ for some $0<\tau<1$.

Keywords: multiplicity, stability, semilinear elliptic equation, sublinear growth