# Solvability of Nonlinear Elliptic Type Equation With Two Unrelated Non standard Growths

## TL;DR

This paper investigates the conditions under which nonlinear elliptic equations with complex growth conditions have solutions, using advanced mathematical techniques to establish existence results.

## Contribution

It introduces new sufficient conditions for the existence of solutions to nonlinear elliptic equations with two unrelated non-standard growths.

## Key findings

- Established existence of weak solutions under specified conditions
- Applied monotonicity and compactness methods effectively
- Extended solvability results to more general growth scenarios

## Abstract

In this paper, we study the solvability of the nonlinear Dirichlet problem with sum of the operators of independent non standard growths in a bounded domain $\Omega \subset \mathbb{R}^{n}$. We obtain sufficient conditions and show the existence of weak solutions of the considered problem by using monotonicity and compactness methods together.