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

Mugnai, Dimitri; Papageorgiou, Nikolaos

doi:10.1090/S0002-9947-2013-06124-7

Wang’s multiplicity result for superlinear $(p,q)$–equations without the Ambrosetti–Rabinowitz condition
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by Dimitri Mugnai and Nikolaos S. Papageorgiou PDF

Trans. Amer. Math. Soc. 366 (2014), 4919-4937 Request permission

Abstract:

We consider a nonlinear elliptic equation driven by the sum of a $p$–Laplacian and a $q$–Laplacian, where $1<q\leq 2\leq p<\infty$ 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.

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