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superlinear problems and quasilinear elliptic equations

Proceedings of the Edinburgh Mathematical Society (1)

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Quasilinear Problems Involving Changing-Sign Nonlinearities without an Ambrosetti–Rabinowitz-Type Condition
Leonelo Iturriaga, Marco A. Souto, Pedro Ubilla
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Proceedings of the Edinburgh Mathematical Society / Volume 57 / Issue 3 / October 2014

Published online by Cambridge University Press:

16 April 2014, pp. 755-762
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In this paper quasilinear elliptic boundary value equations without an Ambrosetti and Rabinowitz growth condition are considered. Existence of a non-trivial solution result is established. For this, we show the existence of a Cerami sequence by using a variant of the mountain-pass theorem due to Schechter. The novelty here is that we may consider nonlinearities that satisfy a local p-superlinear condition and may change sign.