We investigate the solvability of the quasilinear Neumann problem (1.1) with sub- and supercritical exponents in an unbounded domain Ω. Under some integrability conditions on the coefficients we establish embedding theorems of weighted Sobolev spaces into weighted Lebesgue spaces. This is used to obtain solutions through a global minimization of a variational functional.
We investigate a class of Kirchhoff-type equations characterized by critical growth within Orlicz-Sobolev spaces. The main result establishes the existence of infinitely many solutions with negative energy. Using an adapted concentration-compactness principle and advanced variational methods, we overcome key challenges such as non-compactness and non-differentiability to the associated functionals. This work extends existing results to more general functional spaces, offering new insights into nonlocal...
In this paper we prove an estimate for the measure of superlevel sets of weak solutions to quasilinear elliptic systems in divergence form. In some special cases, such an estimate allows us to improve on the integrability of the solution.