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

Dimitri Mugnai, Nikolaos S. Papageorgiou
2013 Transactions of the American Mathematical Society  
We consider a nonlinear elliptic equation driven by the sum of a p-Laplacian and a q-Laplacian, where 1 < q ≤ 2 ≤ p < ∞ with a (p − 1)-superlinear Carathéodory 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 least three nontrivial solutions; among them one is positive and one is negative.
doi:10.1090/s0002-9947-2013-06124-7 fatcat:4yndirixq5esrjytn7jdnpnkyi