caa a22 4500 445843187 CHVBK 20180317145351.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s00526-010-0370-y doi (NATIONALLICENCE)springer-10.1007/s00526-010-0370-y D'Aprile Teresa Dipartimento di Matematica, Università di Roma "Tor Vergata”, via della Ricerca Scientifica 1, 00133, Rome, Italy aut Solutions with many mixed positive and negative interior spikes for a semilinear Neumann problem [Elektronische Daten] [Teresa D'Aprile] We study the existence of sign-changing multiple interior spike solutions for the following Neumann problem $$\varepsilon^2\Delta v-v+f(v) = 0 \,\, {\rm in} \,\, \Omega, \quad \frac{\partial v}{\partial \nu} = 0 \,\, {\rm on} \,\, \partial \Omega,$$where Ω is a smooth bounded domain of $${\mathbb {R}^N}$$ , ε is a small positive parameter, f is a superlinear, subcritical and odd nonlinearity. No symmetry on Ω is assumed. To our knowledge, only positive interior peak solutions have been obtained for this problem and it remains a question whether or not multiple interior peak solutions with mixed positive and negative peaks exist. In this paper we assume that Ω is a two-dimensional strictly convex domain and, provided that k is sufficiently large, we construct a (k+1)-peak solutions with k positive interior peaks aligned on a closed curve near ∂Ω and 1 negative interior peak located in a more centered part of Ω. Springer-Verlag, 2010 Calculus of Variations and Partial Differential Equations Springer-Verlag 41/3-4(2011-07-01), 435-454 0944-2669 41:3-4<435 2011 41 526 https://doi.org/10.1007/s00526-010-0370-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-010-0370-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- D'Aprile Teresa Dipartimento di Matematica, Università di Roma "Tor Vergata”, via della Ricerca Scientifica 1, 00133, Rome, Italy aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 41/3-4(2011-07-01), 435-454 0944-2669 41:3-4<435 2011 41 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer