Multiple Small Solutions for Perturbed Nonhomogeneous Quasilinear Elliptic Systems
Existence of multiple small solutions for a quasilinear elliptic system in R^N whose nonhomogeneous differential operator (after C. A. Stuart) depends on both u and its gradient, with a locally sublinear, locally symmetric nonlinearity plus an arbitrary continuous small perturbation with no growth hypothesis. The proof runs a variant of Clark's theorem without global symmetry and extends Moser's iteration to the system, relating sup-norms to L^{2*} norms while handling the nonhomogeneity and the non-compact Sobolev embedding on R^N (arXiv:2501.01602, math.AP).
Multiplicity result on a class of nonhomogeneous quasilinear elliptic system with small
We investigate a class of quasilinear elliptic system involving a nonhomogeneous differential operator which is introduced by C. A. Stuart [Milan J. Math. 79 (2011), 327-341] and depends on not only …