Recent results on (p,q)-Laplacian type equations
Abstract
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. 1
Full text
Recent result s on (p, q)–Laplacian type equat ions Rossel l a Bar t ol o Dipartimento di Meccanica, Matematica e Management Politecnico di Bari [email protected] A bst r act . Starting from a new sum decomposition of W 1,p (R N )∩W 1,q (R N ) and using a variational approach, weinvestigatetheexistence of multiple weak solutions of a (p, q)–Laplacian equation on R N , for 1 < q < p < N , with a sign–changing potential and a Carath´eodory reaction term satisfying the celebrated Ambrosetti– Rabinowitz condition. Our assumptions are mild and different from those used in related papers and moreover our results improve or complement previous ones for the single p–Laplacian. 1