caa a22 4500 445835443 CHVBK 20180317145329.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s00209-010-0686-5 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0686-5 Positive and sign-changing clusters around saddle points of the potential for nonlinear elliptic problems [Elektronische Daten] [Teresa D'Aprile, David Ruiz] We study the existence and asymptotic behavior of positive and sign-changing multipeak solutions for the equation $$ -\varepsilon^2\Delta v+V(x)v=f(v)\quad{\rm in}\,\,\,\mathbb{R}^N, $$ where ε is a small positive parameter, f a superlinear, subcritical and odd nonlinearity, V a uniformly positive potential. No symmetry on V is assumed. It is known (Kang and Wei in Adv Differ Equ 5:899-928, 2000) that this equation has positive multipeak solutions with all peaks approaching a local maximum of V. It is also proved that solutions alternating positive and negative spikes exist in the case of a minimum (see D'Aprile and Pistoia in Ann Inst H. Poincaré Anal Non Linéaire 26:1423-1451, 2009). The aim of this paper is to show the existence of both positive and sign-changing multipeak solutions around a nondegenerate saddle point of V. Springer-Verlag, 2010 Nonlinear elliptic equation nationallicence Saddle point nationallicence Cluster nationallicence Finite-dimensional reduction nationallicence Max-min argument nationallicence D'Aprile Teresa Dipartimento di Matematica, Università di Roma "Tor Vergata”, via della Ricerca Scientifica 1, 00133, Rome, Italy aut Ruiz David Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, Avda. Fuentenueva s/n, 18071, Granada, Spain aut Mathematische Zeitschrift Springer-Verlag 268/3-4(2011-08-01), 605-634 0025-5874 268:3-4<605 2011 268 209 https://doi.org/10.1007/s00209-010-0686-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0686-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- D'Aprile Teresa Dipartimento di Matematica, Università di Roma "Tor Vergata”, via della Ricerca Scientifica 1, 00133, Rome, Italy aut NATIONALLICENCE 700 1- Ruiz David Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, Avda. Fuentenueva s/n, 18071, Granada, Spain aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 268/3-4(2011-08-01), 605-634 0025-5874 268:3-4<605 2011 268 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer