Location of Nodal solutions for quasilinear elliptic equations with gradient dependence
Dumitru Motreanu Viorica V. Motreanu Abdelkrim Moussaoui
Discrete & Continuous Dynamical Systems - S 2018, 11(2): 293-307 doi: 10.3934/dcdss.2018016

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.

keywords: Quasilinear elliptic equations (p, q)-Laplacian gradient dependence nodal solutions constant-sign solutions location sub-supersolutions extremal solutions

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