Location of Nodal solutions for quasilinear elliptic equations with gradient dependence
Location of Nodal solutions for quasilinear elliptic equations with gradient dependence
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.