Lucia, Marcello; Magrone, Paola; Zhou, Huan-Song A Dirichlet problem with asymptotically linear and changing sign nonlinearity. (English) Zbl 1086.35048 Rev. Mat. Complut. 16, No. 2, 465-481 (2003). The authors discuss the existence of positive solutions to the problem \[ -\Delta u= g(x, u),\quad u\in H^1_0(\Omega),\tag{1} \] where \(\Omega\) is a bounded domain of \(\mathbb{R}^d\), \(g(x,s)\) is allowed to change sign and has an asymptotically linear behaviour in \(\delta\) at infinity. Using the mountain pass theorem the authors prove existence of solutions for (1). Reviewer: Messoud A. Efendiev (Berlin) Cited in 3 Documents MSC: 35J60 Nonlinear elliptic equations 35J20 Variational methods for second-order elliptic equations 35J25 Boundary value problems for second-order elliptic equations 47J30 Variational methods involving nonlinear operators Keywords:elliptic equation; mountain pass theorem; asymptotically linear nonlinearity PDFBibTeX XMLCite \textit{M. Lucia} et al., Rev. Mat. Complut. 16, No. 2, 465--481 (2003; Zbl 1086.35048) Full Text: DOI EuDML