Some quasilinear elliptic equations involving multiple $p$-Laplacians

TL;DR

This paper investigates (p,q)-Laplacian equations with nonlinearities using variational methods, establishing existence results for zero mass cases and exploring more general Born-Infeld type quasilinear problems.

Contribution

It provides new existence results for (p,q)-Laplacian equations with zero mass and extends analysis to Born-Infeld type quasilinear problems.

Findings

Existence of solutions for zero mass (p,q)-Laplacian equations.

Application of variational techniques to nonlinear quasilinear problems.

Extension to Born-Infeld type equations.

Abstract

This paper is devoted to the study, with variational technique, of (p,q)-Laplacian equations in presence of general nonlinearities. Especially we obtain the existence result for the zero mass case, which includes a large class of pure power nonlinearities. More general quasilinear problems of Born-Infeld type are also considered.