# On a $(p,q)$-Laplacian problem with parametric concave term and asymmetric perturbation

## TL;DR

This paper studies a Dirichlet problem involving the $(p,q)$-Laplace operator with asymmetric concave reactions, demonstrating the existence of multiple solutions, including positive, negative, nodal, and a sequence of sign-changing solutions converging to zero.

## Contribution

It introduces new existence results for multiple solutions of the $(p,q)$-Laplacian problem with asymmetric perturbations, including a sequence of sign-changing solutions under oddness conditions.

## Key findings

- Four nontrivial solutions are found for small parameters.
- A sequence of sign-changing solutions converging to zero is constructed.
- The results extend understanding of $(p,q)$-Laplacian problems with asymmetric reactions.

## Abstract

A Dirichlet problem driven by the $(p,q)$-Laplace operator and an asymmetric concave reaction with positive parameter is investigated. Four nontrivial smooth solutions (two positive, one negative, and the remaining nodal) are obtained once the parameter turns out to be sufficiently small. Under a oddness condition near the origin for the perturbation, a whole sequence of sign-changing solutions, which converges to zero, is produced.