# A Quasilinear Elliptic Equation with Oscillating Nonlinearity

## TL;DR

This paper establishes the existence of solutions for a quasilinear elliptic equation with oscillating nonlinearities near the origin, expanding understanding of such equations with unbounded nonlinear terms.

## Contribution

It introduces a method to handle unbounded, oscillatory nonlinearities in quasilinear elliptic equations, providing new existence results.

## Key findings

- Existence of solutions under oscillatory nonlinearities.
- Handling unbounded nonlinearities near the origin.
- Extension of solution theory for quasilinear elliptic equations.

## Abstract

We find a solution of a quasilinear elliptic equation with Dirichlet's boundary condition on a smooth bounded domain and involving an unbounded continuous nonlinearity with oscillatory behavior near the origin.