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Anisotropic Quasilinear Elliptic Systems with Homogeneous Critical Nonlinearities
Published 29 Dec 2023 in math.AP | (2312.17737v1)
Abstract: In this work we consider a system of quasilinear elliptic equations driven by an anisotropic $p$-Laplacian. The lower-order nonlinearities are in potential form and exhibit critical Sobolev growth. We exhibit conditions on the coefficients of the differential operator, the domain of the unknown function, and the lower-order nonlinearities under which nontrivial solutions are guaranteed to exist and conditions on these objects under which a nontrivial solution does not exist.
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