Multiplicity of solutions for a class of the quasilinear elliptic equations at resonance

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Nonlinear Nonhomogeneous Robin Problems with Superlinear Reaction Term (2016, background): “Recently there have been some existence and multiplicity results for such equations, see [5, 9, 15, 27, 34, 35, 39, 40].”
Qualitative Phenomena for Some Classes of Quasilinear Elliptic Equations with Multiple Resonance (2014, background): “Compared with [42], our results here are considerably stronger.”
(N,q)‐Laplacian problems with critical Trudinger‐Moser nonlinearities (2014, background): “ations [1, 6], and models of elementary particles [10, 4, 2]. Consequently, quasilinear elliptic boundary value problems involving this operator have been widely studied in the literature (see, e.g., [3, 16, 23, 15] and the references therein). In particular, the critical (p,q)-Laplacian problem ”