We show the existence of nontrivial solutions for a class of quasilinear problems in which the governing operators depend on the unknown function. By using a suitable variational setting and a weak version of the Cerami-Palais-Smale condition, we establish the desired result without assuming that the nonlinear source satisfies the Ambrosetti-Rabinowitz condition.
Candela, A.M., Fragnelli, G., Mugnai, D. (2021). Quasilinear Problems without the Ambrosetti-Rabinowitz Condition. MINIMAX THEORY AND ITS APPLICATIONS, 6(2), 239-250.
Quasilinear Problems without the Ambrosetti-Rabinowitz Condition
Fragnelli, Genni;
2021-01-01
Abstract
We show the existence of nontrivial solutions for a class of quasilinear problems in which the governing operators depend on the unknown function. By using a suitable variational setting and a weak version of the Cerami-Palais-Smale condition, we establish the desired result without assuming that the nonlinear source satisfies the Ambrosetti-Rabinowitz condition.
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https://hdl.handle.net/11365/1279787