Multiplicity results for a class of semilinear elliptic equations on \(\mathbb{R}^ m\) (Q2563976)

Existence and multiplicity results are proved for solutions of the problem \[ -\Delta u+u=f(x,u), \quad u\in H^1 (\mathbb{R}^m) \] where \(m\geq 1\) and \(f\) satisfies suitable subcritical and periodic assumptions. In the proofs the mountain pass theorem and the concentration-compactness method are used.