Abstract

We present some multiplicity results concerning semilinear elliptic Dirichlet problems with jumping nonlinearities where the jumping condition involves a set of high eigenvalues not including the first one. Using a variational method we show that the number of solutions may be arbitrarily large provided the number of jumped eigenvalues is large enough. Indeed, we prove that for every positive integer k there exists a positive integer n(k) such that, if the number of jumped eigenvalues is greater than n(k), then the problem has at least a solution which presents k peaks. Moreover, we describe the asymptotic behaviour of the solutions as the number of jumped eigenvalues tends to infinity; in particular, we analyse some concentration phenomena of the peaks (near points or suitable manifolds), we describe the asymptotic profile of the rescaled peaks, etc …

Autore Pugliese

• Passaseo Donato

Tutti gli autori

• R. Molle , D. Passaseo

Titolo volume/Rivista

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

Anno di pubblicazione

2014

ISSN

0944-2669

ISBN

Non Disponibile

Numero di citazioni Wos

5

Ultimo Aggiornamento Citazioni

28/04/2018

Numero di citazioni Scopus

4

Ultimo Aggiornamento Citazioni

28/04/2018

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile