Critical fractional elliptic equations with exponential growth without Ambrosetti-Rabinowitz type condition

2020/04/06 by Hamilton Bueno, Bueno, Hamilton, Eduardo Huerto Caqui +3
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Nonlinear Differential Equations Analysis #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2004.02578

Abstract

In this paper we establish, using variational methods combined with the Moser-Trudinger inequality, existence and multiplicity of weak solutions for a class of critical fractional elliptic equations with exponential growth without a Ambrosetti-Rabinowitz-type condition. The interaction of the nonlinearities with the spectrum of the fractional operator will used to study the existence and multiplicity of solutions. The main technical result proves that a local minimum in C_s⁰(Ω) is also a local minimum in W^s,p₀ for nonlinearities with exponential growth.

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