Start ing from a new sum decomposit ion of W1,p(RN ) ∩W1,q(RN ) and using
a variat ional approach, we invest igate the existence of mult ipleweak solut ions of
a (p, q)–Laplacian equat ion on RN , for 1 < q < p < N , with a sign–changing potent
ial and a Carath´eodory react ion term sat isfying the celebrated Ambroset t i–
Rabinowitz condit ion. Our assumpt ions are mild and different from those used
in related papers and moreover our results improve or complement previous ones
for the single p–Laplacian.
1Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech
