We consider a nonlinear elliptic equation driven by the sum of a $p$--Laplacian and a $q$--Laplacian where $1<q\leq2\leq p<\infty$ with a $(p-1)$--superlinear Carath\'eodory reaction term which doesn't satisfy the usual Ambrosetti--Rabinowitz condition. Using variational methods based on critical point theory together with techniques from Morse theory, we show that the problem has at leat three nontrivial solutions; among them one is positive and one is negative.

Wang’s multiplicity result for superlinear $(p,q)$–equations without the Ambrosetti–Rabinowitz condition

MUGNAI, Dimitri;
2014

Abstract

We consider a nonlinear elliptic equation driven by the sum of a $p$--Laplacian and a $q$--Laplacian where $1
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1232503
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 117
  • ???jsp.display-item.citation.isi??? 112
social impact