Multiplicity results for superlinear elliptic problems with partial interference with the spectrum (Q1081023)

It is proved that if \(\lambda\) is not equal to any of the eigenvalues of \[ -\Delta v=\lambda v\quad in\quad \Omega,\quad v=0\quad on\quad \partial \Omega, \] where \(\Omega \subset R^ N\) (N\(\geq 2)\) is a bounded domain, then the superlinear elliptic boundary value problems \[ -\Delta u- (u^+)^ p-\lambda u=h\quad in\quad \Omega,\quad u=0\quad on\quad \partial \Omega \] where \(u^+=\max \{u,0\}\), \(1<p<(N+2)(N-2)^{-1}\) if \(N\geq 3\) and \(1<p<\infty\), if \(N=2\), \(h\in L_ 2(\Omega)\), for some functions n having more than one solution.