Quasilinear Problems Involving Changing-Sign Nonlinearities without an Ambrosetti–Rabinowitz-Type Condition
Leonelo Iturriaga, Marco A. Souto, Pedro Ubilla
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Source: Crossref
Published: Apr 16, 2014
DOI: 10.1017/s0013091513000667
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Abstract 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.
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