CAUCHY PROBLEM FOR A PARABOLIC–HYPERBOLIC EQUATION WITH NON-CHARACTERISTIC LINE OF TYPE CHANGING
Mathematical Methods in the Applied Sciences. John Wiley and Sons Ltd. 2022.
In this paper, we consider a class of quasilinear stationary Kirchhoff type potential systems with Neumann Boundary conditions, which involves a general variable exponent elliptic operator with critical growth. Under some suitable conditions on the nonlinearities, we establish existence and multiplicity of solutions for the problem by using the concentration-compactness principle of Lions for variable exponents and the mountain pass theorem without the Palais–Smale condition. © 2022 Informa UK Limited, trading as Taylor & Francis Group.