We are concerned with the multiplicity of solutions of the
following singularly perturbed semilinear elliptic equations
in bounded domains $\Omega$:$-\varepsilon^2\Delta u+a(\cdot) u = u|u|^{p-2}$ in $\Omega$ , $u > 0$ in $\Omega$ , $u = 0$ on $\partial\Omega$ . The main purpose of this
paper is to discuss the relationship between the multiplicity of
solutions and the profile of $a(\cdot)$ from the variational point
of view. It is shown that if $a$ has a “peak” in $\Omega$ , then (P) has at least three solutions for sufficiently small $\varepsilon$ .