Abstract. Based on a new Liouville theorem, we study a superlinear Ambrosetti-Prodi problem for the p-Laplacian operator, 1 < p < N. For this, we use the sub and supersolution method, blow up technique and the Leray-Schauder degree theory.
Key words Leray-Schauder degree, sub-supersolutions, viscosity solutions, multiplicity of solutions MSC (2010) 35B45, 47H11, 35J25In this work we study an Ambrosetti-Prodi type problem for an elliptic system involving p-Laplacian operator. The sub and supersolution method and the Leray-Schauder Degree Theory are used in order to prove our result.
The main scope of this paper is to obtain Aleksandrov–Bakelman–Pucci estimates (ABP estimates) for viscosity solutions of singular fully nonlinear operator, which includes the p-Laplacian operator, p > 1.
This work has objective to obtain results of existence and multiplicity of solutions for an Ambrosetti–Prodi-type problem for the [Formula: see text] operator. Moreover, it was proved a continuity result for the parameter which limits the existence of solutions in relation of the parameter [Formula: see text].
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