Existence of multiple solutions for a nonhomogeneous semilinear elliptic equation involving critical exponent (Q765076)

This paper deals with the problem \( -\Delta u + u = u^{2^*-1} + \lambda (f(x,u) + h(x)) \) in \(\mathbb{R}^N\), \(u \in H^1(\mathbb{R}^N)\), \(u>0\) in \(\mathbb{R}^N\), for \(N\geq 5\), \(\lambda >0\), \(2^* = \frac{2N}{N-2}\). The authors provide conditions on \(\lambda\), \(f\) and \(h\) for nonexistence, existence and multiplicity of solutions of the problem above.