Winter, Matthias; Wei, Juncheng Multi-peak solutions for a wide class of singular perturbation problems. (English) Zbl 0922.35025 J. Lond. Math. Soc., II. Ser. 59, No. 2, 585-606 (1999). We are concerned with a wide class of singular perturbation problems arising from diverse fields such as phase transitions, chemotaxis, pattern formation, population dynamics and chemical reaction theory. We study the corresponding elliptic equations in a bounded domain without any symmetry assumptions. We assume that the mean curvature of the boundary has \(\overline{M}\) isolated, non-degenerate critical points. Then we show that for any positive integer \(m\leq\overline{M}\) there exists a stationary solution with \(M\) local peaks which are attained on the boundary and which lie close to these critical points. Our method is based on Lyapunov-Schmidt reduction. Reviewer: M.Winter (Stuttgart) Cited in 21 Documents MSC: 35B40 Asymptotic behavior of solutions to PDEs 35B45 A priori estimates in context of PDEs 35J40 Boundary value problems for higher-order elliptic equations Keywords:phase transitions; elliptic equations; stationary solution; critical points; Lyapunov-Schmidt reduction PDFBibTeX XML Full Text: DOI