It is established the existence of at least one solution for the semilinear elliptic problem \[ -\triangle u + u = \lambda|u|^{q-2}u-h(x)|u|^{p-2}u, \qquad u > 0 \quad \text{in }\mathbb{R}^N, \] where \(h > 0\) is a continuous function on \(\mathbb{R}^N\) satisfying \(\int_{\mathbb{R}^N} h^{q/(q-p)} dx 0.\) If \(0 0\) is a parameter.