Perera, Kanishka; Schechter, Martin Nontrivial solutions of elliptic semilinear equations at resonance. (English) Zbl 0958.35051 Manuscr. Math. 101, No. 3, 301-311 (2000). The authors consider the following Dirichlet problem \(-\Delta u = \lambda_m +f(x,u)\) in a bounded domain \(\Omega\) with smooth boundary, where \(\lambda _m\) is an eigenvalue of the Laplacian operator in \(\Omega\) with Dirichlet boundary data. They treat the doubly resonant case, both at infinity and zero, \(\lim_{t\to 0}f(x,t)/t= \lim_{t\to \infty}f(x,t)/t=0\). They use critical groups computations to get their existence results. Reviewer: Youssef Jabri (Oujda) Cited in 5 Documents MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces 49K27 Optimality conditions for problems in abstract spaces Keywords:double resonance; critical groups PDFBibTeX XMLCite \textit{K. Perera} and \textit{M. Schechter}, Manuscr. Math. 101, No. 3, 301--311 (2000; Zbl 0958.35051) Full Text: DOI