On some nonlinear operators, fixed-point theorems and nonlinear equations

TL;DR

This paper investigates the solvability of certain nonlinear equations, including those with p-Laplacian, using a new approach to study nonlinear continuous operators and their fixed points in Banach spaces.

Contribution

It introduces a novel method for analyzing the solvability of nonlinear equations and fixed points of continuous operators in Banach spaces.

Findings

Established conditions for the solvability of nonlinear equations with p-Laplacian.

Reduced general results for continuous operators on Banach spaces.

Proved existence of fixed points under various conditions.

Abstract

In this article we discuss the solvability of some class of fully nonlinear equations, and equations with p-Laplacian in more general conditions by using a new approach given in [1] for studying the nonlinear continuous operator. Moreover we reduce certain general results for the continuous operators acting on Banach spaces, and investigate their image. Here we also consider the existence of a fixed-point of the continuous operators under various conditions.