Multiplicity of Solutions for a Class of Elliptic Problem of - Laplacian Type with a - Gradient Term

Zakariya Chaouai and Soufiane Maatouk

International Journal of Mathematics and Mathematical Sciences, 2019, vol. 2019, 1-10

Abstract:

We consider the following problem: where is a bounded set in ( ) with a smooth boundary, , , , and and belong to for some . In this paper, we assume that a.e. in and without sign condition and then we prove the existence of at least two bounded solutions under the condition that and are suitably small. For this purpose, we use the Mountain Pass theorem, on an equivalent problem to with variational structure. Here, the main difficulty is that the nonlinearity term considered does not satisfy Ambrosetti and Rabinowitz condition. The key idea is to replace the former condition by the nonquadraticity condition at infinity .

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:6824502

DOI: 10.1155/2019/6824502

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