Signed solutions for a semilinear elliptic problem. (Q1978216)

The author proves the existence of signed solutions with positive energy of the problem \[ \Delta u + p^2_+ - u^q_- = 0 \;\text{in} \;\Omega , \;0 < q < 1 < p, \;p < \frac {N+2}{N-2}, \] \(N>2\), \(\Omega \subset \mathbb R^N\) is bounded and ``sufficiently large''. The proof is based on the study of the dynamical system associated with the corresponding parabolic problem and it can be extended to more general problems.