Existence results for nonlinear anisotropic elliptic partial differential equations with variable exponents

Abstract

    The focus of this paper will be on studying the existence of solutions in the sense of distribution, for a class of nonlinear partial differential equations defined by a variable exponent anisotropic elliptic operator with a growth condition given by a strictly positive continuous real function. The functional setting involves variable exponents anisotropic Sobolev spaces. Mathematics Subject Classification (2010): 35J60, 35J66, 35J67. Received 28 January 2025; Accepted 10 June 2025