Dancer, E. N. Stable and finite Morse index solutions on \(\mathbb R^n\) or on bounded domains with small diffusion. II. (English) Zbl 1183.35125 Indiana Univ. Math. J. 53, No. 1, 97-108 (2004). Abstract: “We study the stable and finite Morse index positive solutions of weakly nonlinear Dirichlet problems with small diffusion on bounded domains in \(\mathbb R^3\).” Similar results as in part I [Trans. Am. Math. Soc. 357, No. 3, 1225–1243 (2005; Zbl 1145.35369)] are obtained under weaker assumptions. Cited in 1 ReviewCited in 14 Documents MSC: 35J60 Nonlinear elliptic equations 35B25 Singular perturbations in context of PDEs 35B35 Stability in context of PDEs 35J25 Boundary value problems for second-order elliptic equations 47J30 Variational methods involving nonlinear operators 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces Citations:Zbl 1145.35369 PDFBibTeX XMLCite \textit{E. N. Dancer}, Indiana Univ. Math. J. 53, No. 1, 97--108 (2004; Zbl 1183.35125) Full Text: DOI