Spectrum and bifurcation for semilinear elliptic problems in RN

This paper is concerned with the following semilinear elliptic problem{−Δu=λm(x)f(u)inRN,u→0as|x|→+∞, where λ is a real parameter and m is a weight function which may be sign-changing. For the linear case, i.e., f(u)=u, we investigate the spectral structure. For the semilinear case, we study the existence and asymptotic behavior of one-sign and nodal solutions by bifurcation method.