Corpus ID: 207852592

Highly quasilinear problems without the Ambrosetti-Rabinowitz condition

  title={Highly quasilinear problems without the Ambrosetti-Rabinowitz condition},
  author={Anna Maria Candela and Genni Fragnelli and Dimitri Mugnai},
  journal={arXiv: Analysis of PDEs},
  • Anna Maria Candela, Genni Fragnelli, Dimitri Mugnai
  • Published 2019
  • Mathematics
  • arXiv: Analysis of PDEs
  • We show the existence of nontrivial solutions for a class of highly 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.