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Stable and finite Morse index solutions on \(\mathbb R^n\) or on bounded domains with small diffusion. II. (English) Zbl 1183.35125

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.

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
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