LOCATION OF NODAL SOLUTIONS FOR QUASILINEAR ELLIPTIC EQUATIONS WITH GRADIENT DEPENDENCE

摘要

Existence and regularity results for quasilinear elliptic equations driven by (p, q)-Laplacian and with gradient dependence are presented. A location principle for nodal (i.e., sign-changing) solutions is obtained by means of constant-sign solutions whose existence is also derived. Criteria for the existence of extremal solutions are finally established.