Oscillatory perturbations of linear problems at resonance (Q1121447)

This paper presents results on bounded perturbations of resonant linear elliptic equations. For certain types of bounded domains \(\Omega \subset {\mathbb{R}}^ n\), \(n\geq 2\), the Dirichlet problem \[ \Delta u+\lambda_ 1u+g(u)=h(x),\quad x\in \Omega;\quad u=0,\quad x\in \partial \Omega \] has infinitely many positive solutions, where \(\lambda_ 1\) is the principal eigenvalue of -\(\Delta\), g a nontrivial periodic nonlinearity of zero mean and h satisfies \(\int_{\Omega}h(x)\phi (x)dx=0\) where \(\phi\) is an eigenfunction corresponding to \(\lambda_ 1\).