On some nonlinear operators, fixed-point theorems and nonlinear equations
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.
Cite
@article{arxiv.1208.2571,
title = {On some nonlinear operators, fixed-point theorems and nonlinear equations},
author = {Kamal N. Soltanov},
journal= {arXiv preprint arXiv:1208.2571},
year = {2012}
}
Comments
12 pages, LaTeX-2e style; Here we reduce a general result on the determination of the image of the continuous map acting in Banach space, and also conduct some result on the existence of the fixed-point. We shows also that this general result is a generalization of the known Lax-Milgram theorem in some sense. Moreover we study some nonlinear BVP